Write a quadratic equation that has the following pair of solutions: {3, 7}.?
150601
Pythag was close, actually it's x^2 - 10x + 21 = 0.
919864
1.  ax + xb\n2.  21x^3 + 24x*2y\n3.  24x^2 + 31x + 10\n4.  24x^2 - 8x - 6\n5.  40x^3 + 66x^2 + 38x + 6\n6.  x^2 - 1\n7.  x^3 - 8
612720
-2 = 1/(1+x)-3/(x-1)\nmultiply both sides by (x^2-1)=(x+1)*(x-1):\n\n-2(x^2-1)= x-1 -3(x+1) \n\nrearrange\n2x^2 - 2x - 6 = 0\ndivide by 2\nx^2 - x -3 =0\napply formula for quadratic equations\nx=(1 +/- sqrt(1+4*3))/2\n = 0.5 +/- sqrt(13)/2\n\n"+/-" means plus or minus (there are two solutions)\n"^2" means squared
783870
7x^2+16x over (x-2)(x+2)(x+3)
854860
(3x - a)(x - 2)(x - 7) = \n(3x - a)(x^2 - 7x - 2x + 14) = \n(3x - a)(x^2 - 9x + 14) = \n3x^3 - 27x^2 + 42x - ax^2 + 18ax - 14a\n3x^3 + (-27 - a)x^2 + (42 + 18a)x - 14a\n\n3x^3 - 32x^2 + 81\n\nso\n\n(-27 - a)x^2 + (42 + 18a)x - 14a = -32x^2 + 81\n(-27 + 32 - a)x^2 + (42 + 18a)x + (-14a - 81) = 0\n(5 - a)x^2 + (42 + 18a)x - (14a + 81) = 0\n(-a + 5)x^2 + (18a + 42)x - (14a + 81) = 0\n-(a - 5)x^2 + (18a + 42)x - (14a + 81) = 0\n\nx = (-b ± sqrt(b^2 - 4ac))/(2a)\n\nx = (-(18a + 42) ± sqrt((18a + 42)^2 - 4(-(a - 5)(-(14a + 81)))/(2(-(a - 5))\n\nx = (-(18a + 42) ± sqrt(((18a + 42)(18a + 42)) - 4(a - 5)(14a + 81)))/(-2(a - 5))\n\nx = (-(18a + 42) ± sqrt((324a^2 + 756a + 756a + 1764) - 4(14a^2 + 81a - 70a - 405))) / (-2(a - 5))\n\nx = (-(18a + 42) ± sqrt(324a^2 + 1512a + 1764 - 4(14a^2 + 9a - 405))) / (-2(a - 5))\n\nx = (-(18a + 42) ± sqrt(324a^2 + 1512a + 1764 - 56a^2 - 36a + 1620))) / (-2(a - 5))\n\nx = (-(18a + 42) ± sqrt(268a^2 + 1476a + 3384)) / (-2(a - 5))\n\nx = (-6(3a + 14) ± sqrt(4(67a^2 + 369a + 846)))/(-2(a - 5))\n\nx = (-6(3a + 14) ± 2sqrt(67a^2 + 369a + 846)) / (-2(a - 5))\n\nx = (3(3a + 14) ± sqrt(67a^2 + 369a + 846))/(a - 5)\n\nUnless you mistyped something, 3x^3 - 32x^2 + 81 does not factor into (3x - a)(x - 2)(x - 7)\n\n--------------------------------------------------------------------------------\n\nx^3 - x^2 + 16x - 16\n(x^3 - x^2) + (16x - 16)\nx^2(x - 1) + 16(x - 1)\n(x^2 + 16)(x - 1)\n\nif you were to take this further, then\n\n(x - 4i)(x + 4i)(x - 1)
848564
Substitute 2x-1 for y in the middle part, you get:\nx^2 + x -6(2x-1) = 2x-1\nThis you can reduce to a quadratic equation for x.
932079
7P = (14x + 21y - 14)A + (21x + 14y + 35)B\n3Q = (-3x + 12y - 6)A + (9x - 12y + 21)B\nAs they are equal, then the coeficients of each A and B are equal:\n14x+21y-14 = 21x+14y+35    and\n3x+12y-6 = 9x-12y+21\nwhich gives you two equations in two unknowns.  The rest is easy.
1160760
what you have is something like\na(b+c)\n\nthe solution is \nab+ac\n\n(x^3)(2x^-2)+(x^3)(4x)\nnow to multiply x^a * x^b you get x^(a+b)\n\n2x^((3+(-2))+4x^(3+1)\n\n2x+4x^4
893823
Use the quadratic equation \n\nt = -b + or - sqr(b^2 - 4ac)/2a\n\nyour equation is already in the form:\n\nat^2 + bt + c = 0\n\njust plug in the variables and solve for t twice
937737
3a2(a-b) -6a(a-b) +21(a-b)\n(a-b)(3a^2-6a+21)\n3(a-b)(a^2-2a+7)
683580
y^2 + 7y + 3y + 21\ny^2 + (7 + 3)y + 21\ny^2 + 10y + 21\n(y + 7)*(y + 3)
806483
Write down all the possible pairs which multiply to 70\nand pick out that pair which sums to 17.\nOr, try to solve the system\nx + y = 17\nxy = 70.\nSo y = x/70,\nx + 70/x = 17.\nNow multiply each term by x and solve the\nresulting quadratic.\nGood luck!
1053403
Write it as:\n2x^2-4x+3x-6\n=2x[x-2]+3[x-2]\n=[2x+3][x-2]\nSimple middle-term factorisation!!!
578331
Solution:\n\n2x*2-3x-14=0\n\nAnswer will be: (2x-7)(x+2)\n\nWhen you multiple these two equations together, you'll do the reverse to start out with your answer.
123892
3(x – 2)^2 – 3(x – 2) – 6\n3((x-2)^2 - (x-2) -2)\n3(x^2-4x+4-x+2-2)\n3(x^2-5x+4)\n\n3(x-4)(x-1)\n\nYay!!
373728
Some folks seem to have forgotten this is a quadratic, and they have two (2) roots!\n\n(x - 7)^2 = 64\n\nx - 7 = ± 8 (take the square root of both sides)\n\nso \n\nx = 7 + 8 = 15 \n\nor \n\nx = 7 - 8 = -1\n\nyou could expand this out and use the quadratic equation to solve it as well:\n\nx^2 - 14x + 49 = 64\n\nx^2 -14x - 15 = 0  a = 1 b = -14  c = -15\n\nthe rest is left to the student as an exercise. :^)
651993
Here's the best I can do to help with the first one.\n   __x_+9___\nx-2)X^2+7x-2\n    x^2-2x\n    ------\n        9x-2\n        9x-18\n        -----\n           16\nFollow the example for the rest