2x^2=-4x+30

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Solution for 2x^2=-4x+30 equation:


Simplifying
2x2 = -4x + 30

Reorder the terms:
2x2 = 30 + -4x

Solving
2x2 = 30 + -4x

Solving for variable 'x'.

Reorder the terms:
-30 + 4x + 2x2 = 30 + -4x + -30 + 4x

Reorder the terms:
-30 + 4x + 2x2 = 30 + -30 + -4x + 4x

Combine like terms: 30 + -30 = 0
-30 + 4x + 2x2 = 0 + -4x + 4x
-30 + 4x + 2x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-30 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 2x + x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

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

Solution

x = {-5, 3}

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