2(x+5)(x+5)+10=138

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Solution for 2(x+5)(x+5)+10=138 equation:


Simplifying
2(x + 5)(x + 5) + 10 = 138

Reorder the terms:
2(5 + x)(x + 5) + 10 = 138

Reorder the terms:
2(5 + x)(5 + x) + 10 = 138

Multiply (5 + x) * (5 + x)
2(5(5 + x) + x(5 + x)) + 10 = 138
2((5 * 5 + x * 5) + x(5 + x)) + 10 = 138
2((25 + 5x) + x(5 + x)) + 10 = 138
2(25 + 5x + (5 * x + x * x)) + 10 = 138
2(25 + 5x + (5x + x2)) + 10 = 138

Combine like terms: 5x + 5x = 10x
2(25 + 10x + x2) + 10 = 138
(25 * 2 + 10x * 2 + x2 * 2) + 10 = 138
(50 + 20x + 2x2) + 10 = 138

Reorder the terms:
50 + 10 + 20x + 2x2 = 138

Combine like terms: 50 + 10 = 60
60 + 20x + 2x2 = 138

Solving
60 + 20x + 2x2 = 138

Solving for variable 'x'.

Reorder the terms:
60 + -138 + 20x + 2x2 = 138 + -138

Combine like terms: 60 + -138 = -78
-78 + 20x + 2x2 = 138 + -138

Combine like terms: 138 + -138 = 0
-78 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + 10x + x2) = 0

Factor a trinomial.
2((-13 + -1x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-13 + -1x)' equal to zero and attempt to solve: Simplifying -13 + -1x = 0 Solving -13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1x = 0 + 13 -1x = 0 + 13 Combine like terms: 0 + 13 = 13 -1x = 13 Divide each side by '-1'. x = -13 Simplifying x = -13

Subproblem 2

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

Solution

x = {-13, 3}

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