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Simplifying 2x2 + 16x + 14 = 54 Reorder the terms: 14 + 16x + 2x2 = 54 Solving 14 + 16x + 2x2 = 54 Solving for variable 'x'. Reorder the terms: 14 + -54 + 16x + 2x2 = 54 + -54 Combine like terms: 14 + -54 = -40 -40 + 16x + 2x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -40 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 8x + x2) = 0 Factor a trinomial. 2((-10 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-10, 2}
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