2x^2+22x=24

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Solution for 2x^2+22x=24 equation:


Simplifying
2x2 + 22x = 24

Reorder the terms:
22x + 2x2 = 24

Solving
22x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 22x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 22x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 11x + x2) = 0

Factor a trinomial.
2((-12 + -1x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12

Subproblem 2

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

Solution

x = {-12, 1}

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