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Simplifying 14x2 + 15x = -20x2 + 1 Reorder the terms: 15x + 14x2 = -20x2 + 1 Reorder the terms: 15x + 14x2 = 1 + -20x2 Solving 15x + 14x2 = 1 + -20x2 Solving for variable 'x'. Reorder the terms: -1 + 15x + 14x2 + 20x2 = 1 + -20x2 + -1 + 20x2 Combine like terms: 14x2 + 20x2 = 34x2 -1 + 15x + 34x2 = 1 + -20x2 + -1 + 20x2 Reorder the terms: -1 + 15x + 34x2 = 1 + -1 + -20x2 + 20x2 Combine like terms: 1 + -1 = 0 -1 + 15x + 34x2 = 0 + -20x2 + 20x2 -1 + 15x + 34x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -1 + 15x + 34x2 = 0 Factor a trinomial. (-1 + -2x)(1 + -17x) = 0Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(1 + -17x)' equal to zero and attempt to solve: Simplifying 1 + -17x = 0 Solving 1 + -17x = 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 + -17x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -17x = 0 + -1 -17x = 0 + -1 Combine like terms: 0 + -1 = -1 -17x = -1 Divide each side by '-17'. x = 0.05882352941 Simplifying x = 0.05882352941Solution
x = {-0.5, 0.05882352941}
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