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Simplifying 0.5(4x + 2) * x = 36 Reorder the terms: 0.5(2 + 4x) * x = 36 Reorder the terms for easier multiplication: 0.5x(2 + 4x) = 36 (2 * 0.5x + 4x * 0.5x) = 36 (1x + 2x2) = 36 Solving 1x + 2x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 1x + 2x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 1x + 2x2 = 0 Factor a trinomial. (-9 + -2x)(4 + -1x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4.5, 4}
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