x*x+(x-7)*(x-7)=25

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Solution for x*x+(x-7)*(x-7)=25 equation: 


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

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

Reorder the terms:
x2 + (-7 + x)(x + -7) = 25

Reorder the terms:
x2 + (-7 + x)(-7 + x) = 25

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

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

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

Combine like terms: x2 + x2 = 2x2
49 + -14x + 2x2 = 25

Solving
49 + -14x + 2x2 = 25

Solving for variable 'x'.

Reorder the terms:
49 + -25 + -14x + 2x2 = 25 + -25

Combine like terms: 49 + -25 = 24
24 + -14x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
24 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -7x + x2) = 0

Factor a trinomial.
2((3 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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 '(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
Solution
x = {3, 4}

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