(x-7)(x-7)=36

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Solution for (x-7)(x-7)=36 equation: 


Simplifying
(x + -7)(x + -7) = 36

Reorder the terms:
(-7 + x)(x + -7) = 36

Reorder the terms:
(-7 + x)(-7 + x) = 36

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = 36
((-7 * -7 + x * -7) + x(-7 + x)) = 36
((49 + -7x) + x(-7 + x)) = 36
(49 + -7x + (-7 * x + x * x)) = 36
(49 + -7x + (-7x + x2)) = 36

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = 36

Solving
49 + -14x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
49 + -36 + -14x + x2 = 36 + -36

Combine like terms: 49 + -36 = 13
13 + -14x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
13 + -14x + x2 = 0

Factor a trinomial.
(1 + -1x)(13 + -1x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {1, 13}

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