How do I find the constant term that should be added to make this expression a perfect-square trinomial?\n   x2 – 14x
212680
When you say "x2", I assume you mean "x^2" - that's how you say x-squared.\n\nYou have to factor, so use reverse FOIL. Set up:\n\n(__ +/- __) (__ +/- __)\n\nYou know what needs to go in the first blank in each parenth to get x^2 (don't you?), so start there, then addends for -14, then see what happens when you square those addends.\n\nYou can do this.
139665
3(x^4+3x^2-11)\n\nseriously you need to pay attention in class instead of asking people. lol
544956
(A^2+2ab+b^2)/(a+b) + (a^2-b^2)/(a-b) + (a-b)/(a+b)/(a^2-b^2)/a+b)\n(a+b)^2/(a+b)+(a+b)(a-b)/(a-b)+ (a-b)/(a+b)*(a+b)/(a^2-b^2)\na+b+a+b+(a-b)/((a+b)(a-b))\n2a+2b+1/(a-b)\n\nif I got all the ( ) in the right places.
362110
you gotta get it to two sets of parentheses, i don't remember exactly how to do it, but i know it should look like (x+1)(x+1) that's not the right answer, but i kinda remember doing this in school
404469
7x^2+16x over (x-2)(x+2)(x+3)
464165
1. Move the constant to the right side:\nx^2 - 6x = 4\n\n2. Take half of the x coefficient (in this case, -6), square it, and add it to both sides:\nx^2 -6x + 9 = 13\n\n3. Factor the left side to (x + a)^2, where a is the number you just squared:\n(x - 3)^2 = 13\n\n4. Take the square root of both sides, remembering that this will give you both a positive and a negative root:\nx - 3 = +/- sqrt 13\n\n5. Move the constant on the left to the right:\nx = 3 +/- sqrt 13
427163
(12x^2 +16x) - (12x-7)- (4x-5)\n12x^2 +16x -12x +7 -4x +5\n\n12x^2+12\n\nthat is what I got....\nI think you might be able to put 12 on the other side of the = sign and turn it into 12x^2 = -12 and then since both sides have 12 in common you can divide both sides by 12 and you will have x^2 = -1 then you can add 1 to both sides and you will have x^2 +1 but I think I'm getting off track by that point....it's been a while since I had to do this stuff.
220771
(x+3)(2x+4) is incorrect.\n(x+3)(2x+4) = 2x^2 + 10x + 12\nSolution:\nMultiply the coefficient of the x^2 term with the constant.\n2(12) = 24\nYou are looking for factors of 24 that add the 11 (which is the coefficient of the x term).\n(3)(8) = 24\n3 + 8 = 11\nReplace 11x with 3x + 8x\n2x^2 + 11x + 12\n= 2x^2 + 3x + 8x + 12\nFactor by grouping\n(2x^2 + 3x) + (8x+12)\n= x(2x+3) + 4(2x+3)\n= (2x+3)(x+4)\nAnswer: (2x+3)(x+4)\nYou can easily check the answer by Foil.\n(2x+3)(x+4) = (2x)(x) + (2x)(4) + (3)(x) + (3)(4)\n= 2x^2 + 8x + 3x + 12\n= 2x^2 + 11x + 12
398036
You have to find the two polynomials that when multiplied by each other will equal the trinomial.\n\nx2 + 8x - 9\n\n(x + 9) (x - 1)\n\nx*x + -1x + 9x -9\n\nx2 + 8x - 9
302607
Both of your examples are perfect square trinomials.\n\n(ax)^2 + 2(a)(b)x + b^2 = (ax + b)(ax + b) = (ax + b)^2\n\n9y^2 - 48y + 64 \n= (3y)^2 + 2(3)(-8)y + (-8)^2\n= (3y - 8)^2\n\n16x^2 + 24x + 9 \n= (4x)^2 + 2(4)(3)x + 3^2\n= (4x + 3)^2
345274
First you need to make it equal to zero, so add 12x and add 3 to both sides.  You now have 6x^2 + 12x + 3 = 0\n\nThe number in front of x^2 is a (6)\nThe number in front of x is b (12)\nThe number with no variable is c (3)\n\nThe formula is [-b +- sqrt(b^2 - 4ac)] all over 2a\n\nPlug the values into their proper places.  You should have\n\n-12 +- sqrt(144 - 4x6x3) all over 2x6\n\nwhich is -12 +- sqrt(72) all over 12  [the 12 does not cancel here]\n\nYou should simplify the sqrt(72); since 72 = 36X2 this becomes 6 sqrt(2)\n\nThat's -12 +- 6 sqrt(2) all over 12\n\nDivide each term by 6 to simplify (except the sqrt(2))\n\n-2 +- sqrt(2)  all over 2
519848
x^2 - 2(3-x^2)\nDistribute the -2\nx^2 + (-2)(3) + (-2)(-x^2)\nSimplify\n= x^2 - 6 + 2x^2\nCombine like terms\n= 3x^2 - 6
259562
Um...\n\n2(-X) + 3(-X) + X + 8\n\n-2X - 3X + X + 8\n\n-5X + X + 8\n\n-4X + 8\n\n8 - 4X
264544
You simply divide each term in the polynomial by that integer.. For your example here it goes..\n\n(3x^2+8x-2) divided by 2 \n\n> {3(x^2)/2} + {8x/2} - {2/2}\n\n>> Answer: 1.5 x^2 + 4x -1    or   (3/2)x^2 + 4x -1
347375
Alright, don't listen to the above post...\n\nGrade 12 here, answering questions all day for mere fun.\n\n12)\ny - 3 = -1/3 (x + 4)\n\nEXPLAINED\n\nadd 3 to both sides\ny = -1/3 (x + 4) + 3\n\nexpand 1/3(x + 4) \n= x * 1/3 + 4 * -1/3\n= x/3 + 4/3\ny = -1/3x - 4/3 + 3\n\nTo add -4/3 and 3, use 3 = 9/3\ny = -1/3x - 4/3 + 9/3\ny = -1/3x + 5/3\n\nTrue, my bad. I originally added 4/3 instread of -4/3\n\n\n16)\n(-2, -1) (4, -4)\n\nm = Dy / Dx\nm = ((-1) - (-4)) / ((-2) - (4))\nm = 3 / -6\nm = -1/2\n\ny = mx + b\n(-1) = -1/2(-2) + b\n-1 = 1 + b\n-1 - 1 = b\n-2 = b\n\ny = -1/2x - 2\n\nCHECK\ny = -1/2(4) - 2\ny = -2 - 2\ny = -4\nTherefore it works.\n\n18)\n(0, 0) (2, 3)\n\nm = Dy / Dx\nm = ((3) - (0)) / ((2) - (0))\nm = 3/2\n\nb = 0\n\ny = mx + b\ny = (3/2)x + 0\ny = (3/2)x\n\nNote, the lower post copied my answers
34664
Perfect squares between 1 and 49 are:\n1*1=1,\n2*2=4,\n3*3=9,\n4*4=16,\n5*5=25,\n6*6=36,\n7*7=49,\ntherefore \n\n49 = 49\n\nOnly one term is needed
440861
Completing the square involves adding constants to both sides of your equation so you have a form:\n\n(x - a)^2 = b\n\nOnce you get this form, you can take the square root of both sides:\n\nx - a = sqrt(b)\n\nx = a + sqrt(b) \n\nSince a square root can be either positive or negative, it is just as correct to write:\n\nx = a - sqrt(b)\n\nNow, back to the original "perfect square"\n\n(x - a)^2 = b\n\nExpanding this out:\n\nx^2 - 2*a + a^2 = b\n\nMoving b to the other side:\n\nx^2 - 2*a + a^2 - b = 0\n\nYour equation is 2*x^2 - x - 2 = 0\n\nForst thing is to get plain x^2, so divide by 2:\n\nx^2 - (1/2) * x - 1 = 0\n\nNow from the form above, a = 1/.4 because 2*a = (1/2)*x\nNext, look at the constant term: \n \n-1 = a^2 - b\n-1 = (1/4)^2 - b\n\nSolving for b: b = 17/16\n\nSo your perfect square equation is:\n\n(x - 1/4)^2 = 17/16\n\nSolving for x:\n\nx - 1/4 = sqrt(17/16)\n\nx = 1/4 + sqrt(17/16)\nx = 1/4 - sqrt(17/16)\n\nSimplifying slightly:\n\nx = (1 + sqrt(17))/4\nx = (1 - sqrt(17))/4