11x^2-34x-31=4x^2+5+2x

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Solution for 11x^2-34x-31=4x^2+5+2x equation:


Simplifying
11x2 + -34x + -31 = 4x2 + 5 + 2x

Reorder the terms:
-31 + -34x + 11x2 = 4x2 + 5 + 2x

Reorder the terms:
-31 + -34x + 11x2 = 5 + 2x + 4x2

Solving
-31 + -34x + 11x2 = 5 + 2x + 4x2

Solving for variable 'x'.

Reorder the terms:
-31 + -5 + -34x + -2x + 11x2 + -4x2 = 5 + 2x + 4x2 + -5 + -2x + -4x2

Combine like terms: -31 + -5 = -36
-36 + -34x + -2x + 11x2 + -4x2 = 5 + 2x + 4x2 + -5 + -2x + -4x2

Combine like terms: -34x + -2x = -36x
-36 + -36x + 11x2 + -4x2 = 5 + 2x + 4x2 + -5 + -2x + -4x2

Combine like terms: 11x2 + -4x2 = 7x2
-36 + -36x + 7x2 = 5 + 2x + 4x2 + -5 + -2x + -4x2

Reorder the terms:
-36 + -36x + 7x2 = 5 + -5 + 2x + -2x + 4x2 + -4x2

Combine like terms: 5 + -5 = 0
-36 + -36x + 7x2 = 0 + 2x + -2x + 4x2 + -4x2
-36 + -36x + 7x2 = 2x + -2x + 4x2 + -4x2

Combine like terms: 2x + -2x = 0
-36 + -36x + 7x2 = 0 + 4x2 + -4x2
-36 + -36x + 7x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-36 + -36x + 7x2 = 0

Factor a trinomial.
(-6 + -7x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -7x)' equal to zero and attempt to solve: Simplifying -6 + -7x = 0 Solving -6 + -7x = 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 + -7x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7x = 0 + 6 -7x = 0 + 6 Combine like terms: 0 + 6 = 6 -7x = 6 Divide each side by '-7'. x = -0.8571428571 Simplifying x = -0.8571428571

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-0.8571428571, 6}

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