31x=10x^2+15

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Solution for 31x=10x^2+15 equation:


Simplifying
31x = 10x2 + 15

Reorder the terms:
31x = 15 + 10x2

Solving
31x = 15 + 10x2

Solving for variable 'x'.

Reorder the terms:
-15 + 31x + -10x2 = 15 + 10x2 + -15 + -10x2

Reorder the terms:
-15 + 31x + -10x2 = 15 + -15 + 10x2 + -10x2

Combine like terms: 15 + -15 = 0
-15 + 31x + -10x2 = 0 + 10x2 + -10x2
-15 + 31x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-15 + 31x + -10x2 = 0

Factor a trinomial.
(-5 + 2x)(3 + -5x) = 0

Subproblem 1

Set the factor '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5

Subproblem 2

Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6

Solution

x = {2.5, 0.6}

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