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Simplifying (9x2 + 4x + -5) + (-3x2 + 6x + 1) = 0 Reorder the terms: (-5 + 4x + 9x2) + (-3x2 + 6x + 1) = 0 Remove parenthesis around (-5 + 4x + 9x2) -5 + 4x + 9x2 + (-3x2 + 6x + 1) = 0 Reorder the terms: -5 + 4x + 9x2 + (1 + 6x + -3x2) = 0 Remove parenthesis around (1 + 6x + -3x2) -5 + 4x + 9x2 + 1 + 6x + -3x2 = 0 Reorder the terms: -5 + 1 + 4x + 6x + 9x2 + -3x2 = 0 Combine like terms: -5 + 1 = -4 -4 + 4x + 6x + 9x2 + -3x2 = 0 Combine like terms: 4x + 6x = 10x -4 + 10x + 9x2 + -3x2 = 0 Combine like terms: 9x2 + -3x2 = 6x2 -4 + 10x + 6x2 = 0 Solving -4 + 10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 5x + 3x2) = 0 Factor a trinomial. 2((-2 + -1x)(1 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-2, 0.3333333333}
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