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Simplifying 0 = -1x2 + 80x + 900 Reorder the terms: 0 = 900 + 80x + -1x2 Solving 0 = 900 + 80x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -900 = -900 -900 + -80x + x2 = 900 + 80x + -1x2 + -900 + -80x + x2 Reorder the terms: -900 + -80x + x2 = 900 + -900 + 80x + -80x + -1x2 + x2 Combine like terms: 900 + -900 = 0 -900 + -80x + x2 = 0 + 80x + -80x + -1x2 + x2 -900 + -80x + x2 = 80x + -80x + -1x2 + x2 Combine like terms: 80x + -80x = 0 -900 + -80x + x2 = 0 + -1x2 + x2 -900 + -80x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -900 + -80x + x2 = 0 Factor a trinomial. (-10 + -1x)(90 + -1x) = 0Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 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 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10Subproblem 2
Set the factor '(90 + -1x)' equal to zero and attempt to solve: Simplifying 90 + -1x = 0 Solving 90 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + -1x = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -1x = 0 + -90 -1x = 0 + -90 Combine like terms: 0 + -90 = -90 -1x = -90 Divide each side by '-1'. x = 90 Simplifying x = 90Solution
x = {-10, 90}
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