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Simplifying -0.5(32) * x2 + 176x + 0 = 480 Multiply -0.5 * 32 -16x2 + 176x + 0 = 480 Reorder the terms: 0 + 176x + -16x2 = 480 Remove the zero: 176x + -16x2 = 480 Solving 176x + -16x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 176x + -16x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 176x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-30 + 11x + -1x2) = 0 Factor a trinomial. 16((-6 + x)(5 + -1x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 2
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 = 5Solution
x = {6, 5}
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