6x^2=-31x-5

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Solution for 6x^2=-31x-5 equation:


Simplifying
6x2 = -31x + -5

Reorder the terms:
6x2 = -5 + -31x

Solving
6x2 = -5 + -31x

Solving for variable 'x'.

Reorder the terms:
5 + 31x + 6x2 = -5 + -31x + 5 + 31x

Reorder the terms:
5 + 31x + 6x2 = -5 + 5 + -31x + 31x

Combine like terms: -5 + 5 = 0
5 + 31x + 6x2 = 0 + -31x + 31x
5 + 31x + 6x2 = -31x + 31x

Combine like terms: -31x + 31x = 0
5 + 31x + 6x2 = 0

Factor a trinomial.
(5 + x)(1 + 6x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667

Solution

x = {-5, -0.1666666667}

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