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Simplifying 0 = 2x2 + 29x + 50 Reorder the terms: 0 = 50 + 29x + 2x2 Solving 0 = 50 + 29x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + -29x + -2x2 = 50 + 29x + 2x2 + -50 + -29x + -2x2 Reorder the terms: -50 + -29x + -2x2 = 50 + -50 + 29x + -29x + 2x2 + -2x2 Combine like terms: 50 + -50 = 0 -50 + -29x + -2x2 = 0 + 29x + -29x + 2x2 + -2x2 -50 + -29x + -2x2 = 29x + -29x + 2x2 + -2x2 Combine like terms: 29x + -29x = 0 -50 + -29x + -2x2 = 0 + 2x2 + -2x2 -50 + -29x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -50 + -29x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(50 + 29x + 2x2) = 0 Factor a trinomial. -1((25 + 2x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + 2x)' equal to zero and attempt to solve: Simplifying 25 + 2x = 0 Solving 25 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 2x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 2x = 0 + -25 2x = 0 + -25 Combine like terms: 0 + -25 = -25 2x = -25 Divide each side by '2'. x = -12.5 Simplifying x = -12.5Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-12.5, -2}
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