2x^2=-x+15

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Solution for 2x^2=-x+15 equation:


Simplifying
2x2 = -1x + 15

Reorder the terms:
2x2 = 15 + -1x

Solving
2x2 = 15 + -1x

Solving for variable 'x'.

Reorder the terms:
-15 + x + 2x2 = 15 + -1x + -15 + x

Reorder the terms:
-15 + x + 2x2 = 15 + -15 + -1x + x

Combine like terms: 15 + -15 = 0
-15 + x + 2x2 = 0 + -1x + x
-15 + x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-15 + x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -2x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

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

Solution

x = {-3, 2.5}

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