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Simplifying 9x + 3 + -2x2 = 5x2 + 2x + 3 Reorder the terms: 3 + 9x + -2x2 = 5x2 + 2x + 3 Reorder the terms: 3 + 9x + -2x2 = 3 + 2x + 5x2 Add '-3' to each side of the equation. 3 + 9x + -3 + -2x2 = 3 + 2x + -3 + 5x2 Reorder the terms: 3 + -3 + 9x + -2x2 = 3 + 2x + -3 + 5x2 Combine like terms: 3 + -3 = 0 0 + 9x + -2x2 = 3 + 2x + -3 + 5x2 9x + -2x2 = 3 + 2x + -3 + 5x2 Reorder the terms: 9x + -2x2 = 3 + -3 + 2x + 5x2 Combine like terms: 3 + -3 = 0 9x + -2x2 = 0 + 2x + 5x2 9x + -2x2 = 2x + 5x2 Solving 9x + -2x2 = 2x + 5x2 Solving for variable 'x'. Reorder the terms: 9x + -2x + -2x2 + -5x2 = 2x + 5x2 + -2x + -5x2 Combine like terms: 9x + -2x = 7x 7x + -2x2 + -5x2 = 2x + 5x2 + -2x + -5x2 Combine like terms: -2x2 + -5x2 = -7x2 7x + -7x2 = 2x + 5x2 + -2x + -5x2 Reorder the terms: 7x + -7x2 = 2x + -2x + 5x2 + -5x2 Combine like terms: 2x + -2x = 0 7x + -7x2 = 0 + 5x2 + -5x2 7x + -7x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 7x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '7x'. 7x(1 + -1x) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 1}
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