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Simplifying 3x2 + 9x + 5 = 1 + -2x2 Reorder the terms: 5 + 9x + 3x2 = 1 + -2x2 Solving 5 + 9x + 3x2 = 1 + -2x2 Solving for variable 'x'. Reorder the terms: 5 + -1 + 9x + 3x2 + 2x2 = 1 + -2x2 + -1 + 2x2 Combine like terms: 5 + -1 = 4 4 + 9x + 3x2 + 2x2 = 1 + -2x2 + -1 + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 4 + 9x + 5x2 = 1 + -2x2 + -1 + 2x2 Reorder the terms: 4 + 9x + 5x2 = 1 + -1 + -2x2 + 2x2 Combine like terms: 1 + -1 = 0 4 + 9x + 5x2 = 0 + -2x2 + 2x2 4 + 9x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 4 + 9x + 5x2 = 0 Factor a trinomial. (1 + x)(4 + 5x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Divide each side by '5'. x = -0.8 Simplifying x = -0.8Solution
x = {-1, -0.8}
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