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Simplifying 63 = 0.5(2x2 + 10x + 6x + 30) Reorder the terms: 63 = 0.5(30 + 10x + 6x + 2x2) Combine like terms: 10x + 6x = 16x 63 = 0.5(30 + 16x + 2x2) 63 = (30 * 0.5 + 16x * 0.5 + 2x2 * 0.5) 63 = (15 + 8x + 1x2) Solving 63 = 15 + 8x + 1x2 Solving for variable 'x'. Combine like terms: 63 + -15 = 48 48 + -8x + -1x2 = 15 + 8x + 1x2 + -15 + -8x + -1x2 Reorder the terms: 48 + -8x + -1x2 = 15 + -15 + 8x + -8x + 1x2 + -1x2 Combine like terms: 15 + -15 = 0 48 + -8x + -1x2 = 0 + 8x + -8x + 1x2 + -1x2 48 + -8x + -1x2 = 8x + -8x + 1x2 + -1x2 Combine like terms: 8x + -8x = 0 48 + -8x + -1x2 = 0 + 1x2 + -1x2 48 + -8x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 48 + -8x + -1x2 = 0 Factor a trinomial. (4 + -1x)(12 + x) = 0Subproblem 1
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 = 4Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {4, -12}
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