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Simplifying 48x2 = 24 + -84x Solving 48x2 = 24 + -84x Solving for variable 'x'. Reorder the terms: -24 + 84x + 48x2 = 24 + -84x + -24 + 84x Reorder the terms: -24 + 84x + 48x2 = 24 + -24 + -84x + 84x Combine like terms: 24 + -24 = 0 -24 + 84x + 48x2 = 0 + -84x + 84x -24 + 84x + 48x2 = -84x + 84x Combine like terms: -84x + 84x = 0 -24 + 84x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-2 + 7x + 4x2) = 0 Factor a trinomial. 12((-2 + -1x)(1 + -4x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {-2, 0.25}
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