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Simplifying 0 = 8x2 + 59x + 21 Reorder the terms: 0 = 21 + 59x + 8x2 Solving 0 = 21 + 59x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -21 = -21 -21 + -59x + -8x2 = 21 + 59x + 8x2 + -21 + -59x + -8x2 Reorder the terms: -21 + -59x + -8x2 = 21 + -21 + 59x + -59x + 8x2 + -8x2 Combine like terms: 21 + -21 = 0 -21 + -59x + -8x2 = 0 + 59x + -59x + 8x2 + -8x2 -21 + -59x + -8x2 = 59x + -59x + 8x2 + -8x2 Combine like terms: 59x + -59x = 0 -21 + -59x + -8x2 = 0 + 8x2 + -8x2 -21 + -59x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -21 + -59x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 59x + 8x2) = 0 Factor a trinomial. -1((7 + x)(3 + 8x)) = 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 + 8x)' equal to zero and attempt to solve: Simplifying 3 + 8x = 0 Solving 3 + 8x = 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 + 8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8x = 0 + -3 8x = 0 + -3 Combine like terms: 0 + -3 = -3 8x = -3 Divide each side by '8'. x = -0.375 Simplifying x = -0.375Solution
x = {-7, -0.375}
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