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Simplifying 2x2 + x + 4 = 500 Reorder the terms: 4 + x + 2x2 = 500 Solving 4 + x + 2x2 = 500 Solving for variable 'x'. Reorder the terms: 4 + -500 + x + 2x2 = 500 + -500 Combine like terms: 4 + -500 = -496 -496 + x + 2x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -496 + x + 2x2 = 0 Factor a trinomial. (-16 + -1x)(31 + -2x) = 0Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve: Simplifying -16 + -1x = 0 Solving -16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x = 0 + 16 -1x = 0 + 16 Combine like terms: 0 + 16 = 16 -1x = 16 Divide each side by '-1'. x = -16 Simplifying x = -16Subproblem 2
Set the factor '(31 + -2x)' equal to zero and attempt to solve: Simplifying 31 + -2x = 0 Solving 31 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -2x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -2x = 0 + -31 -2x = 0 + -31 Combine like terms: 0 + -31 = -31 -2x = -31 Divide each side by '-2'. x = 15.5 Simplifying x = 15.5Solution
x = {-16, 15.5}
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