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Simplifying 49 = 2x2 + 4x + 1 Reorder the terms: 49 = 1 + 4x + 2x2 Solving 49 = 1 + 4x + 2x2 Solving for variable 'x'. Combine like terms: 49 + -1 = 48 48 + -4x + -2x2 = 1 + 4x + 2x2 + -1 + -4x + -2x2 Reorder the terms: 48 + -4x + -2x2 = 1 + -1 + 4x + -4x + 2x2 + -2x2 Combine like terms: 1 + -1 = 0 48 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 48 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 48 + -4x + -2x2 = 0 + 2x2 + -2x2 48 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 48 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -2x + -1x2) = 0 Factor a trinomial. 2((4 + -1x)(6 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {4, -6}
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