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Simplifying 17x2 + 18x = 11x2 + 3x + 9 Reorder the terms: 18x + 17x2 = 11x2 + 3x + 9 Reorder the terms: 18x + 17x2 = 9 + 3x + 11x2 Solving 18x + 17x2 = 9 + 3x + 11x2 Solving for variable 'x'. Reorder the terms: -9 + 18x + -3x + 17x2 + -11x2 = 9 + 3x + 11x2 + -9 + -3x + -11x2 Combine like terms: 18x + -3x = 15x -9 + 15x + 17x2 + -11x2 = 9 + 3x + 11x2 + -9 + -3x + -11x2 Combine like terms: 17x2 + -11x2 = 6x2 -9 + 15x + 6x2 = 9 + 3x + 11x2 + -9 + -3x + -11x2 Reorder the terms: -9 + 15x + 6x2 = 9 + -9 + 3x + -3x + 11x2 + -11x2 Combine like terms: 9 + -9 = 0 -9 + 15x + 6x2 = 0 + 3x + -3x + 11x2 + -11x2 -9 + 15x + 6x2 = 3x + -3x + 11x2 + -11x2 Combine like terms: 3x + -3x = 0 -9 + 15x + 6x2 = 0 + 11x2 + -11x2 -9 + 15x + 6x2 = 11x2 + -11x2 Combine like terms: 11x2 + -11x2 = 0 -9 + 15x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 5x + 2x2) = 0 Factor a trinomial. 3((-3 + -1x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-3, 0.5}
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