(x+5)(x+5)+11(x+5)+18=0

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Solution for (x+5)(x+5)+11(x+5)+18=0 equation:


Simplifying
(x + 5)(x + 5) + 11(x + 5) + 18 = 0

Reorder the terms:
(5 + x)(x + 5) + 11(x + 5) + 18 = 0

Reorder the terms:
(5 + x)(5 + x) + 11(x + 5) + 18 = 0

Multiply (5 + x) * (5 + x)
(5(5 + x) + x(5 + x)) + 11(x + 5) + 18 = 0
((5 * 5 + x * 5) + x(5 + x)) + 11(x + 5) + 18 = 0
((25 + 5x) + x(5 + x)) + 11(x + 5) + 18 = 0
(25 + 5x + (5 * x + x * x)) + 11(x + 5) + 18 = 0
(25 + 5x + (5x + x2)) + 11(x + 5) + 18 = 0

Combine like terms: 5x + 5x = 10x
(25 + 10x + x2) + 11(x + 5) + 18 = 0

Reorder the terms:
25 + 10x + x2 + 11(5 + x) + 18 = 0
25 + 10x + x2 + (5 * 11 + x * 11) + 18 = 0
25 + 10x + x2 + (55 + 11x) + 18 = 0

Reorder the terms:
25 + 55 + 18 + 10x + 11x + x2 = 0

Combine like terms: 25 + 55 = 80
80 + 18 + 10x + 11x + x2 = 0

Combine like terms: 80 + 18 = 98
98 + 10x + 11x + x2 = 0

Combine like terms: 10x + 11x = 21x
98 + 21x + x2 = 0

Solving
98 + 21x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(14 + x)(7 + x) = 0

Subproblem 1

Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14

Subproblem 2

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Solution

x = {-14, -7}

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