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Simplifying 0 = 4x2 + 31x + 21 Reorder the terms: 0 = 21 + 31x + 4x2 Solving 0 = 21 + 31x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -21 = -21 -21 + -31x + -4x2 = 21 + 31x + 4x2 + -21 + -31x + -4x2 Reorder the terms: -21 + -31x + -4x2 = 21 + -21 + 31x + -31x + 4x2 + -4x2 Combine like terms: 21 + -21 = 0 -21 + -31x + -4x2 = 0 + 31x + -31x + 4x2 + -4x2 -21 + -31x + -4x2 = 31x + -31x + 4x2 + -4x2 Combine like terms: 31x + -31x = 0 -21 + -31x + -4x2 = 0 + 4x2 + -4x2 -21 + -31x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -21 + -31x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 31x + 4x2) = 0 Factor a trinomial. -1((7 + x)(3 + 4x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
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 = -0.75Solution
x = {-7, -0.75}
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