Calculate the value of (b² - 4ac) in the equation "9x² + 12x + 16 = 0" and state how many real solutions this
156633
the value you need is 12*12-4*9*16 = 144-576 = -432\n\nBecause it is negative, the equation has NO real solutions.
586490
x²+2ax+(a²-b²-c²)=0\n\nhere, I will change: \na = m\nb = n\nc = o\nso that you will not get confuse.\nit will be :x²+2mx+(m²-n²-0²)=0\n\nto make sure that the equation is always real\nwe have to look at b²-4ac (you know this right?)solution:\n\nb²-4ac = 4m²-4(m²-n²-o²)\n=4m²-4m²+4n²+4o²\n=4n²+4o²\n\nhere you see, if a negative number is squared, it would be a positive number eg (-2)²=4\neven if n and o is negative,they will be positive when squared. so we got 4(n²+o²)>=0, it is proven that the roots are always real.\n\nif you still can't understand this, message me
412551
-4x+16=-1-4x\n-4x+4x=-16-1\n0=-17\n\nthe answer is [a]0
736802
Initial concentration B: 8/20=0.4 M\nInitial concentration C: 12/20= 0.6 M\n\n.. .. .. .. .. .. 2A <=> B + C\nInitial .. .. .. .. .. .. .. 0.4 .. 0.6\nReact .. .. .. .. .. .. .. x .. ..x\nProduce ..  2x\nAt Equil. .. . 2x .. ..0.4-x.. 0.6-x\n\nK=[B][C]/[A]^2 =>\n0.035=(0.4-x)(0.6-x)/(2x)^2 =>\n0.035*4x^2= 0.24 -0.4x -0.6x + x^2 =>\n0.86x^2 -x+0.24 =0\nIt is a quadratic equation of the type ax^2+bx+c=0\nThere are two possible solutions:\n\nx1= (-b+Squareroot( b^2-4ac))/2a\nx2= (-b-Squareroot( b^2-4ac))/2a\n\nx1 =(-(-1)+ SQRT( (-1)^2 -4*0.86*0.24) ) / (2*0.86)= 0.824\nx2=0.339\n\nx1 is rejected since it is bigger than the concentration of B which is the limiting reagent (and also bigger of C) and we can't have negative values for the equilibrium concentration of B (and C)\nThus the only acceptable solution is x=x2= 0.339\n[A]=2*x= 2*0.339= 0.678 M
693019
8(16) = 128\n\nx^29squared) + 10x\n\nmove all terms to same side x^2 + 10x -128 = 0\n\nuse quadratic equation: -b +/- (plus or minus) the square root of b^2 - 4ac.\n\nThis would make x equal to 7.3693168.... it is an irrational number- i had to take the square root of 612. but if you round x is equal to about 7 or -7
736851
I got a different answer than you.  Let's do this together:\n\nRecall that for an equation ax² + bx + c = 0, that the quadratic formula is:\n\nx = [ -b ± √ (b² - 4ac) ] ÷ 2a\n\nSo we want to find the zeros of x² + 10x + 23\n\nSo, x = [ -b ± √ (b² - 4ac) ] ÷ 2a\n\n= [ -10 ± √ (10² - 4*1*23) ] ÷ 2*1\n\n= [ -10 ± √ (100 - 92) ] ÷ 2\n\n= [ -10 ± √8 ] ÷ 2\n\n= [ -10 ± 2√2 ] ÷ 2\n\n= -5 ±√2\n\nHope that helped.\n\n~ ♥ ~
798499
Given ax² + bx + c = 0, the quadratic formula tells us that:\n\nx = [ -b ± √(b²-4ac) ] ÷ 2a\n\nIn your problem, a=3, b=12, c=1  --  simply plug these values into the quadratic formula to solve for x.
824781
9u^2-24u+16=0\ndiscriminant\n=(-24)^2-4*9*16\n=0\nsince it is = 0\nso its roots are real and\nequal
617358
x = (-b +- sqrt(b^2-4ac))/(2a)\n\nThis equation solves the quadratic equation, where\n\nax^2 + bx + c = 0.
429058
x==(-b+/-sqrt(b^2-4ac))/(2a).
202779
This is quadratic. A quadratic equation looks like:\nax^2+bx+c = 0\n\nSo a=4, b=-1, and c=3\n\nSo by using the quadratic equation: \n\nx= (-b+sqrt(b^2-4ac))/2a\nand\nx= (-b-sqrt(b^2-4ac))/2a\n\nTry to get the answer from that.... note that imaginary numbers may be involved!
752254
Well, let's check if y=4.\nJust replace y with 4\n4(4) + 2(4) = 24\n16 + 8 = 24\n24 = 24 \nThis is equation is true, so you are correct.
508006
x^2 + 4bx + 2b=0\n(x+2b)^2 - 4b^2 + 2b = 0\n(x+2b)^2 = 4b^2 - 2b\n(x+2b) = SQRT(4b^2 - 2b)\nx = [SQRT(4b^2 - 2b)]-2b\n\n3x^2 -bx +1=0\n3(x^2 - (b/3)x + (1/3)) = 0\nx^2 - (b/3)x + (1/3) = 0\n(x-(b/6))^2 -(b/6)^2 + (1/3) = 0\n(x-(b/6))^2 = (b/6)^2 - (1/3)\nx-(b/6) = SQRT[b^2/36 - 12/36]\nx-(b/6) = [SQRT{^2 - 12)] / 6\nx = {[SQRT{^2 - 12)]+b} / 6\n\nb^2x^2 - 2bx + c^2= 0\n(bx)^2 - 2(bx) + c^2 = 0\n(bx-1)^2 - 1 + c^2 = 0\n(bx-1)^2 = 1 - c^2\nbx-1 = SQRT(1-c^2)\nbx = SQRT(1-c^2)+1\nx = [SQRT(1-c^2)+1]/b
126044
Stand on your head.\n\n16=8+8 and you haven't even changed the equation...(including what direction it's facing)
55048
9b+4(8c+c)-54=15c-13b+5\n\n9b+32c+4c-54=15c-13b+5\n\n9b+36c-54=15c-13b+5\n\n9b+21c-54=(-13b)+5\n\n21c-54=(-22b)+5\n\n21c=(-22b)+59\n\nc=(-22b+59)/21
792411
put y = 7 and x =4 and solve for c\nwe get 7 = 16+c or c = -9
839760
The roots are 0 and -16/5\n\nTo solve any quadratic equation eg. ax^2+bx+c, you can apply formula x= (-b+-sqrt(b^2-4ac))/2a