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Simplifying (5x2 + 2x + -3) + -1(-5x2 + 4x + 5) + (-2x2 + -3x + -5) = 0 Reorder the terms: (-3 + 2x + 5x2) + -1(-5x2 + 4x + 5) + (-2x2 + -3x + -5) = 0 Remove parenthesis around (-3 + 2x + 5x2) -3 + 2x + 5x2 + -1(-5x2 + 4x + 5) + (-2x2 + -3x + -5) = 0 Reorder the terms: -3 + 2x + 5x2 + -1(5 + 4x + -5x2) + (-2x2 + -3x + -5) = 0 -3 + 2x + 5x2 + (5 * -1 + 4x * -1 + -5x2 * -1) + (-2x2 + -3x + -5) = 0 -3 + 2x + 5x2 + (-5 + -4x + 5x2) + (-2x2 + -3x + -5) = 0 Reorder the terms: -3 + 2x + 5x2 + -5 + -4x + 5x2 + (-5 + -3x + -2x2) = 0 Remove parenthesis around (-5 + -3x + -2x2) -3 + 2x + 5x2 + -5 + -4x + 5x2 + -5 + -3x + -2x2 = 0 Reorder the terms: -3 + -5 + -5 + 2x + -4x + -3x + 5x2 + 5x2 + -2x2 = 0 Combine like terms: -3 + -5 = -8 -8 + -5 + 2x + -4x + -3x + 5x2 + 5x2 + -2x2 = 0 Combine like terms: -8 + -5 = -13 -13 + 2x + -4x + -3x + 5x2 + 5x2 + -2x2 = 0 Combine like terms: 2x + -4x = -2x -13 + -2x + -3x + 5x2 + 5x2 + -2x2 = 0 Combine like terms: -2x + -3x = -5x -13 + -5x + 5x2 + 5x2 + -2x2 = 0 Combine like terms: 5x2 + 5x2 = 10x2 -13 + -5x + 10x2 + -2x2 = 0 Combine like terms: 10x2 + -2x2 = 8x2 -13 + -5x + 8x2 = 0 Solving -13 + -5x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(13 + -8x) = 0Subproblem 1
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 = -1Subproblem 2
Set the factor '(13 + -8x)' equal to zero and attempt to solve: Simplifying 13 + -8x = 0 Solving 13 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -8x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8x = 0 + -13 -8x = 0 + -13 Combine like terms: 0 + -13 = -13 -8x = -13 Divide each side by '-8'. x = 1.625 Simplifying x = 1.625Solution
x = {-1, 1.625}
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