(x-7)(x-7)=16

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Solution for (x-7)(x-7)=16 equation: 


Simplifying
(x + -7)(x + -7) = 16

Reorder the terms:
(-7 + x)(x + -7) = 16

Reorder the terms:
(-7 + x)(-7 + x) = 16

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = 16
((-7 * -7 + x * -7) + x(-7 + x)) = 16
((49 + -7x) + x(-7 + x)) = 16
(49 + -7x + (-7 * x + x * x)) = 16
(49 + -7x + (-7x + x2)) = 16

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = 16

Solving
49 + -14x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
49 + -16 + -14x + x2 = 16 + -16

Combine like terms: 49 + -16 = 33
33 + -14x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
33 + -14x + x2 = 0

Factor a trinomial.
(3 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {3, 11}

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