4x^2=31x-21

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Solution for 4x^2=31x-21 equation:


Simplifying
4x2 = 31x + -21

Reorder the terms:
4x2 = -21 + 31x

Solving
4x2 = -21 + 31x

Solving for variable 'x'.

Reorder the terms:
21 + -31x + 4x2 = -21 + 31x + 21 + -31x

Reorder the terms:
21 + -31x + 4x2 = -21 + 21 + 31x + -31x

Combine like terms: -21 + 21 = 0
21 + -31x + 4x2 = 0 + 31x + -31x
21 + -31x + 4x2 = 31x + -31x

Combine like terms: 31x + -31x = 0
21 + -31x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(7 + -1x) = 0

Subproblem 1

Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {0.75, 7}

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