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Simplifying 4x2 = 2x2 + 17x + -30 Reorder the terms: 4x2 = -30 + 17x + 2x2 Solving 4x2 = -30 + 17x + 2x2 Solving for variable 'x'. Reorder the terms: 30 + -17x + 4x2 + -2x2 = -30 + 17x + 2x2 + 30 + -17x + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 30 + -17x + 2x2 = -30 + 17x + 2x2 + 30 + -17x + -2x2 Reorder the terms: 30 + -17x + 2x2 = -30 + 30 + 17x + -17x + 2x2 + -2x2 Combine like terms: -30 + 30 = 0 30 + -17x + 2x2 = 0 + 17x + -17x + 2x2 + -2x2 30 + -17x + 2x2 = 17x + -17x + 2x2 + -2x2 Combine like terms: 17x + -17x = 0 30 + -17x + 2x2 = 0 + 2x2 + -2x2 30 + -17x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + -17x + 2x2 = 0 Factor a trinomial. (5 + -2x)(6 + -1x) = 0Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {2.5, 6}
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