(x-7)(x-7)=169

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Solution for (x-7)(x-7)=169 equation: 


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

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

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

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

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

Solving
49 + -14x + x2 = 169

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(-6 + -1x)(20 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-6, 20}

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