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Simplifying 0 = 84x2 + 91x + 21 Reorder the terms: 0 = 21 + 91x + 84x2 Solving 0 = 21 + 91x + 84x2 Solving for variable 'x'. Combine like terms: 0 + -21 = -21 -21 + -91x + -84x2 = 21 + 91x + 84x2 + -21 + -91x + -84x2 Reorder the terms: -21 + -91x + -84x2 = 21 + -21 + 91x + -91x + 84x2 + -84x2 Combine like terms: 21 + -21 = 0 -21 + -91x + -84x2 = 0 + 91x + -91x + 84x2 + -84x2 -21 + -91x + -84x2 = 91x + -91x + 84x2 + -84x2 Combine like terms: 91x + -91x = 0 -21 + -91x + -84x2 = 0 + 84x2 + -84x2 -21 + -91x + -84x2 = 84x2 + -84x2 Combine like terms: 84x2 + -84x2 = 0 -21 + -91x + -84x2 = 0 Factor out the Greatest Common Factor (GCF), '-7'. -7(3 + 13x + 12x2) = 0 Factor a trinomial. -7((3 + 4x)(1 + 3x)) = 0 Ignore the factor -7.Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-0.75, -0.3333333333}
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