4x^2=31x+8

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Solution for 4x^2=31x+8 equation:


Simplifying
4x2 = 31x + 8

Reorder the terms:
4x2 = 8 + 31x

Solving
4x2 = 8 + 31x

Solving for variable 'x'.

Reorder the terms:
-8 + -31x + 4x2 = 8 + 31x + -8 + -31x

Reorder the terms:
-8 + -31x + 4x2 = 8 + -8 + 31x + -31x

Combine like terms: 8 + -8 = 0
-8 + -31x + 4x2 = 0 + 31x + -31x
-8 + -31x + 4x2 = 31x + -31x

Combine like terms: 31x + -31x = 0
-8 + -31x + 4x2 = 0

Factor a trinomial.
(-1 + -4x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-0.25, 8}

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