(x-7)(x-7)+(x-14)(x-14)=x*x

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Solution for (x-7)(x-7)+(x-14)(x-14)=x*x equation: 


Simplifying
(x + -7)(x + -7) + (x + -14)(x + -14) = x * x

Reorder the terms:
(-7 + x)(x + -7) + (x + -14)(x + -14) = x * x

Reorder the terms:
(-7 + x)(-7 + x) + (x + -14)(x + -14) = x * x

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) + (x + -14)(x + -14) = x * x
((-7 * -7 + x * -7) + x(-7 + x)) + (x + -14)(x + -14) = x * x
((49 + -7x) + x(-7 + x)) + (x + -14)(x + -14) = x * x
(49 + -7x + (-7 * x + x * x)) + (x + -14)(x + -14) = x * x
(49 + -7x + (-7x + x2)) + (x + -14)(x + -14) = x * x

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

Reorder the terms:
49 + -14x + x2 + (-14 + x)(x + -14) = x * x

Reorder the terms:
49 + -14x + x2 + (-14 + x)(-14 + x) = x * x

Multiply (-14 + x) * (-14 + x)
49 + -14x + x2 + (-14(-14 + x) + x(-14 + x)) = x * x
49 + -14x + x2 + ((-14 * -14 + x * -14) + x(-14 + x)) = x * x
49 + -14x + x2 + ((196 + -14x) + x(-14 + x)) = x * x
49 + -14x + x2 + (196 + -14x + (-14 * x + x * x)) = x * x
49 + -14x + x2 + (196 + -14x + (-14x + x2)) = x * x

Combine like terms: -14x + -14x = -28x
49 + -14x + x2 + (196 + -28x + x2) = x * x

Reorder the terms:
49 + 196 + -14x + -28x + x2 + x2 = x * x

Combine like terms: 49 + 196 = 245
245 + -14x + -28x + x2 + x2 = x * x

Combine like terms: -14x + -28x = -42x
245 + -42x + x2 + x2 = x * x

Combine like terms: x2 + x2 = 2x2
245 + -42x + 2x2 = x * x

Multiply x * x
245 + -42x + 2x2 = x2

Solving
245 + -42x + 2x2 = x2

Solving for variable 'x'.

Combine like terms: 2x2 + -1x2 = 1x2
245 + -42x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
245 + -42x + 1x2 = 0

Factor a trinomial.
(7 + -1x)(35 + -1x) = 0


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(35 + -1x)' equal to zero and attempt to solve:

Simplifying
35 + -1x = 0

Solving
35 + -1x = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1x = 0 + -35
-1x = 0 + -35

Combine like terms: 0 + -35 = -35
-1x = -35

Divide each side by '-1'.
x = 35

Simplifying
x = 35
Solution
x = {7, 35}

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