How would i model the below problem with a quadratic equation and solve? I dont understand it..?
361839
Here's the answer:\n\nV=1/3hx^2\n\nYou know that h=15ft, so\n\nV=2880ft^3=1/3(15ft)x^2\n576ft^2=x^2\nx=24ft\n\nThe length of one side of the base is 24 feet.
915753
To help solve for t you'll need to use the quadratic formula. It's too difficult to show how I got the answer since I can't use the correct symbols, but the answer is t = 1.39.
939068
Is this one problem?  If so, you can solve it like this:\n\n(a/b) / (c/d) = (a/b) * (d/c)\n\n~ ~ ~ ~ \n\n( (x² - 4) / x² ) / ( (x²+5x+6) / x ) = \n\n( (x² - 4) / x² ) * ( x / (x²+5x+6) ) = \n\n( (x² - 4) * x) ) / (x² * (x²+5x+6) ) = \n\n( (x² - 4)  / (x * (x²+5x+6) ) = \n\n{{ now notice you can factor your quadratic equations, to get the following }}\n\n(x+2)(x-2)  / (x * (x+2)(x+3) ) = \n\n(x-2) / (x(x+3))\n\nHope that helped!\n\n~ ♥ ~
952054
To find the equation, just substitute the 2 roots to the "Quadramagic formula" (...)\nx² - (p + q)x + pq = 0\nwhere p and q are the roots.\n\nHence, p = 7 + i and q = 7 - i.  We substitute:\nx² - [(7 + i) + (7 - i)]x + (7 + i)(7 - i) = 0\n\nWe add and multiply\nx² - (14)x + (7² - i²) = 0\n\nSince i² = -1, then\nx² - 14x + 49 - (-1) = 0\n\nthen,\nx² - 14x + 49 + 1 = 0\n\nTherefore, the quadratic equation is\nx² - 14x + 50 = 0\n\nTherefore, the correct answer is 1).\n\n^_^
870960
Do you mean that the roots of x^2+pX+r are α  and β and you need to find quadratics in terms of p and q?\nIf so you can use the following:\nIn any quadratic ax^2 + bx + c = 0, the sum of the roots = -b/a and the product of the roots = c/a.\nUsing this,  -(α + β) = p, and αβ= r.\n\nAnswers are for terms b and c in the quadratic x^2 + bx + c\ni)\nb = -(1/α + 1/β) = -(α + β)/αβ = p/r\nc = 1/αβ = 1/r\n\nii) \nb = -(1/α^2 + 1/β^2) =  -(α^2 + β^2)/(αβ)^2 = -[(α + β)^2 - 2αβ])/(αβ)^2 = -(p^2 - 2r)/r^2\nc = 1/(αβ)^2 = 1/r^2\n\niii) \nb = (α^2β + αβ^2) = αβ(α + β) = -pr\nc = -α^2β * -αβ^2 = (αβ)^3 = r^3
259003
Use the quadratic formula.  It works everytime!\nx = (-b plus or minus sprt(b^2 - 4ac))/2\nwhere\nax^2 + bx + c = 0\nSome of these will factor, however not all of them will.
285238
you can take 9v^2 out and then it becomes a simple quadratic equation\ni can give u d ans \nit will be\n\n9v^2(v+2)(v+1)\ni hope u understood
670824
There are 2 ways to solve for this \n\n1. Separating the x^2\n\n2. Quadratic Formula\n   ax^2 + bx + c = 0\n x = (-b + or - sqrt(b^2 - 4ac))/2a\n http://www.1728.com/quadrtc.gif\n\n\nSolving it by separating x^2\n\na. First separate x^2\n(x + ?)(x +?)\n\nb. Now we have to figure out the 2 variables that would give us 4x and -12 when we multiply them out. notice, that 4 is positive so the larger number has to be Positive.\n\n-12 = 12 * -1   12x + -1x = 11x\n-12 = 6 * -2    6x + -2x = 4x\n-12 = 4 * -3    4x + -3x = x\n\ntherefore the 2 variables would be 6 and -2\n\n(x + 6)(x - 2) = 0\nSo x, would be either -6, or 2\n---------------------------------------------  \n2. SOLVING USING THE QUADRATIC FORMULA\nThis one is way easier\n\nax^2 + bx + c = 0\nx^2 + 4x - 12 = 0\n\n x = (-b + or - sqrt(b^2 - 4ac))/2a\n x = (-4 + or - sqrt(4^2 - 4*1*-12))/2*1\n\n x = (-4 + or - 8)/2\n x = (-4 + 8)/2 = 2\n\n x - (-4 - 8)/2 = -6
992331
The trick here is to note that it looks like a quadratic formula.  Let's do a little manuevering to see this:\n\nx^4 = (x^2)^2\n\nwhich means that we can re-write the problem as (x^2)^2 + x^2 + 1.  Now, substitute another letter, say t for x^2.  We get:\n\nt^2 + t + 1\n\nAll I've done is replace the two x^2 values with 't'.  Now, it's just a quadratic equation of the form:\n\nax^2 + bx + c\n\nTo factor this, you'll need to find two values that multiply to the last term (1, in this case) and add to the coefficient of the second term (which is also 1, in this case).  \n\nWith a little investigation, you'll find that two integers do not exist with such properties, which for most math books, means that, though the problem has a solution, it can't be factored.\n\n***THE ANSWER STOPS HERE if you haven't learned about imaginary numbers.***\n\n*However*, in case you really want to factor this, you simply use the quadratic formula to find the values of x that solve this equation:\n\nt = (-b +/- sqrt(b^2 - 4ac))/2a\n\nSo, we get that t = (-1 + sqrt(-3))/2 and t = (-1 - sqrt(-3))/2, which are imaginary numbers.  These two solutions I will call solutionone and solutiontwo.  \n\nSo the factorization for f(t) is:\n\n(t - solutionone)(t - solutiontwo) where solutionone and solutiontwo are the values that come out of the quadratic formula:\n\nThen, you plug x^2 back in for t and get:\n\n(x^2 - solutionone)(x^2 - solutiontwo)\n\nThese need to be factored as well (ugh) because a linear factorization implies that all the factors have x instead of x^2.  \n\nThank goodness, though, that these are really easy.\n\nIt is always the case that x^2 - a can be factored like this:\n\n(x - sqrt(a))(x + sqrt(a)).\n\nAlways.\n\nSo, this means that the complete factorization for the problem is:\n\n(x - sqrt(solutionone))(x + sqrt(solutionone))(x - sqrt(solutiontwo))(x + sqrt(solutiontwo))\n\nYeow!  Good luck!
589722
Step 1: Solve one equation for one variable in terms of the other.\nStep 2: Plug that into the other equation and solve for the second variable.\nStep 3: Plug the second variable into the first equation and solve for the first variable.
29264
Yuo can't solve this.Because it is a formula and not an equation..If u assign some value equal to this formula such as 0 u have the solution.
1072562
I'm reading the equation as \n\n4x^2 + 8x -1 = 0\n\nUsing quadratic formula x = (-8 +/- sqrt(64+16))/8 \n\nso x = -18/8 or 2/8 = -9/4 or 1/4\n\nThose are the roots.\n\nSubstitute each of those values as y into the second formula.
705433
Derivation of the quadratic formula by completing the square.\n\nax^2 + bx + c = 0\nx^2 + (b/a)x + (c/a) = 0\nx^2 + (b/a)x = -c/a\nx^2 + (b/a)x + b^2/(4a^2) =  b^2/(4a^2) - c/a \n(x + b/2a)^2 =  b^2/(4a^2) - 4ac/(4a^2) \nx + b/2a = ±√[ b^2/(4a^2) - 4ac/(4a^2) ]\n\nx = -b/2a ± √[ b^2/(4a^2) - 4ac/(4a^2) ]\n= -b/2a ± √[ b^2- 4ac] / 2a\n\nx = {-b ± √[ b^2- 4ac] } / 2a
720929
Let me just work through the steps to solve the problem:\n\nsqrt(2x^2-1)=x   <---Original Equation\n2x^2-1=x         <---Square both sides\n2x^2-x-1=0       <---Subtract x\n\nNow, apply the quadradic equation:\nx=(-b+/-(sqrt(b^2-4ac))/(2a)\n\nFor this equation, the equation is:\nx=(-(-1)+/-(sqrt((-1^2)-4*2*(-1))/(2*(2))\n\nSimplified it is:\nx=(1+/-sqrt(1+8))/(4)\nx=(1+3)/4 or x=(1-3)/4\n\nSo, x=1 or x=-1/2
883463
Quadratic formula:\nX=(-b+Sqrt(b^2-4ac))/2a\nOR\n(-b-Sqrt(b^2-4ac))/2a\n\nIn case you don't know what a,b,&c stand for, they are the coefficients of the quadratic equation (besides c.)... OK, that was kind of condusing, so I'll just write out the quadratic equation, using a,b,&c where the numbers should be:\nax^2-bx+c\n\nIn your case the equation is:\nx^2 -2x +1=5, which is equal to:\n\n(1)x^6 + (-2)x + (-4)= 0, \n(the correct form for a quadratic equation)\nTherefore, a=1,\n                  b=-2\n                  c=-4\nTherefore,\nX=(-b+Sqrt(b^2-4ac))/2a\nOR\n(-b-Sqrt(b^2-4ac))/2a (The Quadratic Equation)\nbecomes:\n\nX=(2+sqrt(4+16))/2 = (2+sqrt(20))/2 = (2+2sqrt(5))/2 = 1+sqrt(5)\nOR \n1-sqrt(5)
82007
Just type in quadratic equation and maybe roots in a serch engine. You will have your pick of dozens of sites.
922434
There is only one step. Take the quadratic formula and plug in the numbers.\n\nIf ax^2 + bx + c = 0,\nx = (-b +/- sqrt(b^2-4ac))/2a\n\nFor the equation you gave, a=1, b=19, c=88. Plug those numbers in and see what you get.\n\nIf you're confused by the +/-, it's shorthand for writing two things in one. There are usually two values of x that work, one with + and one with -.