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Simplifying 5(x2 + 1) = 9x2 + -10x + -1 Reorder the terms: 5(1 + x2) = 9x2 + -10x + -1 (1 * 5 + x2 * 5) = 9x2 + -10x + -1 (5 + 5x2) = 9x2 + -10x + -1 Reorder the terms: 5 + 5x2 = -1 + -10x + 9x2 Solving 5 + 5x2 = -1 + -10x + 9x2 Solving for variable 'x'. Reorder the terms: 5 + 1 + 10x + 5x2 + -9x2 = -1 + -10x + 9x2 + 1 + 10x + -9x2 Combine like terms: 5 + 1 = 6 6 + 10x + 5x2 + -9x2 = -1 + -10x + 9x2 + 1 + 10x + -9x2 Combine like terms: 5x2 + -9x2 = -4x2 6 + 10x + -4x2 = -1 + -10x + 9x2 + 1 + 10x + -9x2 Reorder the terms: 6 + 10x + -4x2 = -1 + 1 + -10x + 10x + 9x2 + -9x2 Combine like terms: -1 + 1 = 0 6 + 10x + -4x2 = 0 + -10x + 10x + 9x2 + -9x2 6 + 10x + -4x2 = -10x + 10x + 9x2 + -9x2 Combine like terms: -10x + 10x = 0 6 + 10x + -4x2 = 0 + 9x2 + -9x2 6 + 10x + -4x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 6 + 10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 5x + -2x2) = 0 Factor a trinomial. 2((3 + -1x)(1 + 2x)) = 0 Ignore the factor 2.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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