(x-7)(x-7)=9

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Solution for (x-7)(x-7)=9 equation: 


Simplifying
(x + -7)(x + -7) = 9

Reorder the terms:
(-7 + x)(x + -7) = 9

Reorder the terms:
(-7 + x)(-7 + x) = 9

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = 9
((-7 * -7 + x * -7) + x(-7 + x)) = 9
((49 + -7x) + x(-7 + x)) = 9
(49 + -7x + (-7 * x + x * x)) = 9
(49 + -7x + (-7x + x2)) = 9

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = 9

Solving
49 + -14x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
49 + -9 + -14x + x2 = 9 + -9

Combine like terms: 49 + -9 = 40
40 + -14x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
40 + -14x + x2 = 0

Factor a trinomial.
(4 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {4, 10}

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