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Simplifying 5 + 2x = 10x2 + 35x + 25 Reorder the terms: 5 + 2x = 25 + 35x + 10x2 Solving 5 + 2x = 25 + 35x + 10x2 Solving for variable 'x'. Reorder the terms: 5 + -25 + 2x + -35x + -10x2 = 25 + 35x + 10x2 + -25 + -35x + -10x2 Combine like terms: 5 + -25 = -20 -20 + 2x + -35x + -10x2 = 25 + 35x + 10x2 + -25 + -35x + -10x2 Combine like terms: 2x + -35x = -33x -20 + -33x + -10x2 = 25 + 35x + 10x2 + -25 + -35x + -10x2 Reorder the terms: -20 + -33x + -10x2 = 25 + -25 + 35x + -35x + 10x2 + -10x2 Combine like terms: 25 + -25 = 0 -20 + -33x + -10x2 = 0 + 35x + -35x + 10x2 + -10x2 -20 + -33x + -10x2 = 35x + -35x + 10x2 + -10x2 Combine like terms: 35x + -35x = 0 -20 + -33x + -10x2 = 0 + 10x2 + -10x2 -20 + -33x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -20 + -33x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 33x + 10x2) = 0 Factor a trinomial. -1((5 + 2x)(4 + 5x)) = 0 Ignore the factor -1.Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Divide each side by '5'. x = -0.8 Simplifying x = -0.8Solution
x = {-2.5, -0.8}
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