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Simplifying 486 = 90x + 4x2 Solving 486 = 90x + 4x2 Solving for variable 'x'. Reorder the terms: 486 + -90x + -4x2 = 90x + -90x + 4x2 + -4x2 Combine like terms: 90x + -90x = 0 486 + -90x + -4x2 = 0 + 4x2 + -4x2 486 + -90x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 486 + -90x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(243 + -45x + -2x2) = 0 Factor a trinomial. 2((9 + -2x)(27 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Subproblem 2
Set the factor '(27 + x)' equal to zero and attempt to solve: Simplifying 27 + x = 0 Solving 27 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + x = 0 + -27 x = 0 + -27 Combine like terms: 0 + -27 = -27 x = -27 Simplifying x = -27Solution
x = {4.5, -27}
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