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Simplifying 4x2 + -150 = 5x2 + 25x Reorder the terms: -150 + 4x2 = 5x2 + 25x Reorder the terms: -150 + 4x2 = 25x + 5x2 Solving -150 + 4x2 = 25x + 5x2 Solving for variable 'x'. Reorder the terms: -150 + -25x + 4x2 + -5x2 = 25x + 5x2 + -25x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -150 + -25x + -1x2 = 25x + 5x2 + -25x + -5x2 Reorder the terms: -150 + -25x + -1x2 = 25x + -25x + 5x2 + -5x2 Combine like terms: 25x + -25x = 0 -150 + -25x + -1x2 = 0 + 5x2 + -5x2 -150 + -25x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -150 + -25x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(150 + 25x + x2) = 0 Factor a trinomial. -1((15 + x)(10 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {-15, -10}
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