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Simplifying 0 = -2x2 + -25x + 75 Reorder the terms: 0 = 75 + -25x + -2x2 Solving 0 = 75 + -25x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -75 = -75 -75 + 25x + 2x2 = 75 + -25x + -2x2 + -75 + 25x + 2x2 Reorder the terms: -75 + 25x + 2x2 = 75 + -75 + -25x + 25x + -2x2 + 2x2 Combine like terms: 75 + -75 = 0 -75 + 25x + 2x2 = 0 + -25x + 25x + -2x2 + 2x2 -75 + 25x + 2x2 = -25x + 25x + -2x2 + 2x2 Combine like terms: -25x + 25x = 0 -75 + 25x + 2x2 = 0 + -2x2 + 2x2 -75 + 25x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -75 + 25x + 2x2 = 0 Factor a trinomial. (-15 + -1x)(5 + -2x) = 0Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 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 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 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 = {-15, 2.5}
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