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Simplifying 4x2 = 9x2 + -72x + 144 Reorder the terms: 4x2 = 144 + -72x + 9x2 Solving 4x2 = 144 + -72x + 9x2 Solving for variable 'x'. Reorder the terms: -144 + 72x + 4x2 + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Combine like terms: 4x2 + -9x2 = -5x2 -144 + 72x + -5x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Reorder the terms: -144 + 72x + -5x2 = 144 + -144 + -72x + 72x + 9x2 + -9x2 Combine like terms: 144 + -144 = 0 -144 + 72x + -5x2 = 0 + -72x + 72x + 9x2 + -9x2 -144 + 72x + -5x2 = -72x + 72x + 9x2 + -9x2 Combine like terms: -72x + 72x = 0 -144 + 72x + -5x2 = 0 + 9x2 + -9x2 -144 + 72x + -5x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -144 + 72x + -5x2 = 0 Factor a trinomial. (-12 + x)(12 + -5x) = 0Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 2
Set the factor '(12 + -5x)' equal to zero and attempt to solve: Simplifying 12 + -5x = 0 Solving 12 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5x = 0 + -12 -5x = 0 + -12 Combine like terms: 0 + -12 = -12 -5x = -12 Divide each side by '-5'. x = 2.4 Simplifying x = 2.4Solution
x = {12, 2.4}
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