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Simplifying 5x2 + 25x = 9 + -1x2 Reorder the terms: 25x + 5x2 = 9 + -1x2 Solving 25x + 5x2 = 9 + -1x2 Solving for variable 'x'. Reorder the terms: -9 + 25x + 5x2 + x2 = 9 + -1x2 + -9 + x2 Combine like terms: 5x2 + x2 = 6x2 -9 + 25x + 6x2 = 9 + -1x2 + -9 + x2 Reorder the terms: -9 + 25x + 6x2 = 9 + -9 + -1x2 + x2 Combine like terms: 9 + -9 = 0 -9 + 25x + 6x2 = 0 + -1x2 + x2 -9 + 25x + 6x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -9 + 25x + 6x2 = 0 Factor a trinomial. (-9 + -2x)(1 + -3x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-4.5, 0.3333333333}
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