SOLUTION: factoring (not using the quadratic equation!!) x^2-20x+100 6a^2-11a+3 3a^2= 7a+6 x^2=2x+63

Question 53385: factoring (not using the quadratic equation!!)
x^2-20x+100

6a^2-11a+3

3a^2= 7a+6
x^2=2x+63

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
x^2 - 20x + 100 ~> factors of that sum to ~> -10 and -10
x^2 - 10x - 10x + 100
(x^2 - 10x) + (-10x + 100)
x(x - 10) - 10(x - 10)
(x - 10)(x - 10)
~~
6a^2 - 11a + 3 ~> factors of that sum ~> -9 and -2
6a^2 - 9a - 2a + 3
(6a^2 - 9a) + (-2a + 3)
3a(2a - 3) - 1(2a - 3)
(3a - 1)(2a - 3)
~~
3a^2 = 7a + 6
3a^2 - 7a - 6 = 0 ~> factors of that sum to ~> -9 and 2
3a^2 - 9a + 2a - 6 = 0
(3a^2 - 9a) + (2a - 6) = 0
3a(a - 3) + 2(a - 3) = 0
(3a + 2)(a - 3) = 0
a = -2/3 and a = 3
~~
x^2 = 2x + 63
x^2 - 2x - 63 = 0 ~> factors of that sum to ~> -9 and 7
x^2 - 9x + 7x - 63 = 0
(x^2 - 9x) + (7x - 63) = 0
x(x - 9) + 7(x - 9) = 0
(x + 7)(x - 9) = 0
x = -7 and x = 9
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