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Simplifying 0 = 2x2 + 19x + 35 Reorder the terms: 0 = 35 + 19x + 2x2 Solving 0 = 35 + 19x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -35 = -35 -35 + -19x + -2x2 = 35 + 19x + 2x2 + -35 + -19x + -2x2 Reorder the terms: -35 + -19x + -2x2 = 35 + -35 + 19x + -19x + 2x2 + -2x2 Combine like terms: 35 + -35 = 0 -35 + -19x + -2x2 = 0 + 19x + -19x + 2x2 + -2x2 -35 + -19x + -2x2 = 19x + -19x + 2x2 + -2x2 Combine like terms: 19x + -19x = 0 -35 + -19x + -2x2 = 0 + 2x2 + -2x2 -35 + -19x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -35 + -19x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(35 + 19x + 2x2) = 0 Factor a trinomial. -1((7 + x)(5 + 2x)) = 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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Solution
x = {-7, -2.5}
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