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Simplifying 0 = -16x2 + 100x + -84 Reorder the terms: 0 = -84 + 100x + -16x2 Solving 0 = -84 + 100x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 84 = 84 84 + -100x + 16x2 = -84 + 100x + -16x2 + 84 + -100x + 16x2 Reorder the terms: 84 + -100x + 16x2 = -84 + 84 + 100x + -100x + -16x2 + 16x2 Combine like terms: -84 + 84 = 0 84 + -100x + 16x2 = 0 + 100x + -100x + -16x2 + 16x2 84 + -100x + 16x2 = 100x + -100x + -16x2 + 16x2 Combine like terms: 100x + -100x = 0 84 + -100x + 16x2 = 0 + -16x2 + 16x2 84 + -100x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 84 + -100x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(21 + -25x + 4x2) = 0 Factor a trinomial. 4((1 + -1x)(21 + -4x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(21 + -4x)' equal to zero and attempt to solve: Simplifying 21 + -4x = 0 Solving 21 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -4x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -4x = 0 + -21 -4x = 0 + -21 Combine like terms: 0 + -21 = -21 -4x = -21 Divide each side by '-4'. x = 5.25 Simplifying x = 5.25Solution
x = {1, 5.25}
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