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Simplifying 0 = 4x2 + -13x + 9 Reorder the terms: 0 = 9 + -13x + 4x2 Solving 0 = 9 + -13x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + 13x + -4x2 = 9 + -13x + 4x2 + -9 + 13x + -4x2 Reorder the terms: -9 + 13x + -4x2 = 9 + -9 + -13x + 13x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 -9 + 13x + -4x2 = 0 + -13x + 13x + 4x2 + -4x2 -9 + 13x + -4x2 = -13x + 13x + 4x2 + -4x2 Combine like terms: -13x + 13x = 0 -9 + 13x + -4x2 = 0 + 4x2 + -4x2 -9 + 13x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -9 + 13x + -4x2 = 0 Factor a trinomial. (-9 + 4x)(1 + -1x) = 0Subproblem 1
Set the factor '(-9 + 4x)' equal to zero and attempt to solve: Simplifying -9 + 4x = 0 Solving -9 + 4x = 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 + 4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4x = 0 + 9 4x = 0 + 9 Combine like terms: 0 + 9 = 9 4x = 9 Divide each side by '4'. x = 2.25 Simplifying x = 2.25Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {2.25, 1}
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