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Simplifying 34 = 5x2 + -13x + 6 Reorder the terms: 34 = 6 + -13x + 5x2 Solving 34 = 6 + -13x + 5x2 Solving for variable 'x'. Combine like terms: 34 + -6 = 28 28 + 13x + -5x2 = 6 + -13x + 5x2 + -6 + 13x + -5x2 Reorder the terms: 28 + 13x + -5x2 = 6 + -6 + -13x + 13x + 5x2 + -5x2 Combine like terms: 6 + -6 = 0 28 + 13x + -5x2 = 0 + -13x + 13x + 5x2 + -5x2 28 + 13x + -5x2 = -13x + 13x + 5x2 + -5x2 Combine like terms: -13x + 13x = 0 28 + 13x + -5x2 = 0 + 5x2 + -5x2 28 + 13x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 28 + 13x + -5x2 = 0 Factor a trinomial. (4 + -1x)(7 + 5x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve: Simplifying 7 + 5x = 0 Solving 7 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5x = 0 + -7 5x = 0 + -7 Combine like terms: 0 + -7 = -7 5x = -7 Divide each side by '5'. x = -1.4 Simplifying x = -1.4Solution
x = {4, -1.4}
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