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Simplifying 54 = 2x2 + 3x Reorder the terms: 54 = 3x + 2x2 Solving 54 = 3x + 2x2 Solving for variable 'x'. Reorder the terms: 54 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 54 + -3x + -2x2 = 0 + 2x2 + -2x2 54 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 54 + -3x + -2x2 = 0 Factor a trinomial. (9 + -2x)(6 + x) = 0Subproblem 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 '(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 = {4.5, -6}
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