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Simplifying 1000 = 2x2 + 16x + 310 Reorder the terms: 1000 = 310 + 16x + 2x2 Solving 1000 = 310 + 16x + 2x2 Solving for variable 'x'. Combine like terms: 1000 + -310 = 690 690 + -16x + -2x2 = 310 + 16x + 2x2 + -310 + -16x + -2x2 Reorder the terms: 690 + -16x + -2x2 = 310 + -310 + 16x + -16x + 2x2 + -2x2 Combine like terms: 310 + -310 = 0 690 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2 690 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 690 + -16x + -2x2 = 0 + 2x2 + -2x2 690 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 690 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(345 + -8x + -1x2) = 0 Factor a trinomial. 2((15 + -1x)(23 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Subproblem 2
Set the factor '(23 + x)' equal to zero and attempt to solve: Simplifying 23 + x = 0 Solving 23 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + x = 0 + -23 x = 0 + -23 Combine like terms: 0 + -23 = -23 x = -23 Simplifying x = -23Solution
x = {15, -23}
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