(x-7)(x-7)-25=0

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Solution for (x-7)(x-7)-25=0 equation:


Simplifying
(x + -7)(x + -7) + -25 = 0

Reorder the terms:
(-7 + x)(x + -7) + -25 = 0

Reorder the terms:
(-7 + x)(-7 + x) + -25 = 0

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) + -25 = 0
((-7 * -7 + x * -7) + x(-7 + x)) + -25 = 0
((49 + -7x) + x(-7 + x)) + -25 = 0
(49 + -7x + (-7 * x + x * x)) + -25 = 0
(49 + -7x + (-7x + x2)) + -25 = 0

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) + -25 = 0

Reorder the terms:
49 + -25 + -14x + x2 = 0

Combine like terms: 49 + -25 = 24
24 + -14x + x2 = 0

Solving
24 + -14x + x2 = 0

Solving for variable 'x'.

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


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 12}

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