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Simplifying 4x2 + 9x = 2x2 + 5 Reorder the terms: 9x + 4x2 = 2x2 + 5 Reorder the terms: 9x + 4x2 = 5 + 2x2 Solving 9x + 4x2 = 5 + 2x2 Solving for variable 'x'. Reorder the terms: -5 + 9x + 4x2 + -2x2 = 5 + 2x2 + -5 + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 -5 + 9x + 2x2 = 5 + 2x2 + -5 + -2x2 Reorder the terms: -5 + 9x + 2x2 = 5 + -5 + 2x2 + -2x2 Combine like terms: 5 + -5 = 0 -5 + 9x + 2x2 = 0 + 2x2 + -2x2 -5 + 9x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 9x + 2x2 = 0 Factor a trinomial. (-5 + -1x)(1 + -2x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 0.5}
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