5x^2=-55x-150

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Solution for 5x^2=-55x-150 equation:


Simplifying
5x2 = -55x + -150

Reorder the terms:
5x2 = -150 + -55x

Solving
5x2 = -150 + -55x

Solving for variable 'x'.

Reorder the terms:
150 + 55x + 5x2 = -150 + -55x + 150 + 55x

Reorder the terms:
150 + 55x + 5x2 = -150 + 150 + -55x + 55x

Combine like terms: -150 + 150 = 0
150 + 55x + 5x2 = 0 + -55x + 55x
150 + 55x + 5x2 = -55x + 55x

Combine like terms: -55x + 55x = 0
150 + 55x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(30 + 11x + x2) = 0

Factor a trinomial.
5((6 + x)(5 + x)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {-6, -5}

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