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Simplifying 4x2 + 2x + 14 = 520 Reorder the terms: 14 + 2x + 4x2 = 520 Solving 14 + 2x + 4x2 = 520 Solving for variable 'x'. Reorder the terms: 14 + -520 + 2x + 4x2 = 520 + -520 Combine like terms: 14 + -520 = -506 -506 + 2x + 4x2 = 520 + -520 Combine like terms: 520 + -520 = 0 -506 + 2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-253 + x + 2x2) = 0 Factor a trinomial. 2((-23 + -2x)(11 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -2x)' equal to zero and attempt to solve: Simplifying -23 + -2x = 0 Solving -23 + -2x = 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 + -2x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -2x = 0 + 23 -2x = 0 + 23 Combine like terms: 0 + 23 = 23 -2x = 23 Divide each side by '-2'. x = -11.5 Simplifying x = -11.5Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Solution
x = {-11.5, 11}
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