x*x+(x+5)(x+5)=25*25

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Solution for x*x+(x+5)(x+5)=25*25 equation: 


Simplifying
x * x + (x + 5)(x + 5) = 25 * 25

Multiply x * x
x2 + (x + 5)(x + 5) = 25 * 25

Reorder the terms:
x2 + (5 + x)(x + 5) = 25 * 25

Reorder the terms:
x2 + (5 + x)(5 + x) = 25 * 25

Multiply (5 + x) * (5 + x)
x2 + (5(5 + x) + x(5 + x)) = 25 * 25
x2 + ((5 * 5 + x * 5) + x(5 + x)) = 25 * 25
x2 + ((25 + 5x) + x(5 + x)) = 25 * 25
x2 + (25 + 5x + (5 * x + x * x)) = 25 * 25
x2 + (25 + 5x + (5x + x2)) = 25 * 25

Combine like terms: 5x + 5x = 10x
x2 + (25 + 10x + x2) = 25 * 25

Reorder the terms:
25 + 10x + x2 + x2 = 25 * 25

Combine like terms: x2 + x2 = 2x2
25 + 10x + 2x2 = 25 * 25

Multiply 25 * 25
25 + 10x + 2x2 = 625

Solving
25 + 10x + 2x2 = 625

Solving for variable 'x'.

Reorder the terms:
25 + -625 + 10x + 2x2 = 625 + -625

Combine like terms: 25 + -625 = -600
-600 + 10x + 2x2 = 625 + -625

Combine like terms: 625 + -625 = 0
-600 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-300 + 5x + x2) = 0

Factor a trinomial.
2((-20 + -1x)(15 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-20, 15}

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