x^2+(x-7)(x-7)=169

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Solution for x^2+(x-7)(x-7)=169 equation: 


Simplifying
x2 + (x + -7)(x + -7) = 169

Reorder the terms:
x2 + (-7 + x)(x + -7) = 169

Reorder the terms:
x2 + (-7 + x)(-7 + x) = 169

Multiply (-7 + x) * (-7 + x)
x2 + (-7(-7 + x) + x(-7 + x)) = 169
x2 + ((-7 * -7 + x * -7) + x(-7 + x)) = 169
x2 + ((49 + -7x) + x(-7 + x)) = 169
x2 + (49 + -7x + (-7 * x + x * x)) = 169
x2 + (49 + -7x + (-7x + x2)) = 169

Combine like terms: -7x + -7x = -14x
x2 + (49 + -14x + x2) = 169

Reorder the terms:
49 + -14x + x2 + x2 = 169

Combine like terms: x2 + x2 = 2x2
49 + -14x + 2x2 = 169

Solving
49 + -14x + 2x2 = 169

Solving for variable 'x'.

Reorder the terms:
49 + -169 + -14x + 2x2 = 169 + -169

Combine like terms: 49 + -169 = -120
-120 + -14x + 2x2 = 169 + -169

Combine like terms: 169 + -169 = 0
-120 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -7x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(12 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-5, 12}

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