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Simplifying 5x2 + -36x + 81 = x2 + 18x + 81 Reorder the terms: 81 + -36x + 5x2 = x2 + 18x + 81 Reorder the terms: 81 + -36x + 5x2 = 81 + 18x + x2 Add '-81' to each side of the equation. 81 + -36x + -81 + 5x2 = 81 + 18x + -81 + x2 Reorder the terms: 81 + -81 + -36x + 5x2 = 81 + 18x + -81 + x2 Combine like terms: 81 + -81 = 0 0 + -36x + 5x2 = 81 + 18x + -81 + x2 -36x + 5x2 = 81 + 18x + -81 + x2 Reorder the terms: -36x + 5x2 = 81 + -81 + 18x + x2 Combine like terms: 81 + -81 = 0 -36x + 5x2 = 0 + 18x + x2 -36x + 5x2 = 18x + x2 Solving -36x + 5x2 = 18x + x2 Solving for variable 'x'. Reorder the terms: -36x + -18x + 5x2 + -1x2 = 18x + x2 + -18x + -1x2 Combine like terms: -36x + -18x = -54x -54x + 5x2 + -1x2 = 18x + x2 + -18x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 -54x + 4x2 = 18x + x2 + -18x + -1x2 Reorder the terms: -54x + 4x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 -54x + 4x2 = 0 + x2 + -1x2 -54x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -54x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-27 + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-27 + 2x)' equal to zero and attempt to solve: Simplifying -27 + 2x = 0 Solving -27 + 2x = 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 + 2x = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 2x = 0 + 27 2x = 0 + 27 Combine like terms: 0 + 27 = 27 2x = 27 Divide each side by '2'. x = 13.5 Simplifying x = 13.5Solution
x = {0, 13.5}
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