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Simplifying 7x + 32 = 9x2 + -72x + 144 Reorder the terms: 32 + 7x = 9x2 + -72x + 144 Reorder the terms: 32 + 7x = 144 + -72x + 9x2 Solving 32 + 7x = 144 + -72x + 9x2 Solving for variable 'x'. Reorder the terms: 32 + -144 + 7x + 72x + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Combine like terms: 32 + -144 = -112 -112 + 7x + 72x + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Combine like terms: 7x + 72x = 79x -112 + 79x + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Reorder the terms: -112 + 79x + -9x2 = 144 + -144 + -72x + 72x + 9x2 + -9x2 Combine like terms: 144 + -144 = 0 -112 + 79x + -9x2 = 0 + -72x + 72x + 9x2 + -9x2 -112 + 79x + -9x2 = -72x + 72x + 9x2 + -9x2 Combine like terms: -72x + 72x = 0 -112 + 79x + -9x2 = 0 + 9x2 + -9x2 -112 + 79x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -112 + 79x + -9x2 = 0 Factor a trinomial. (-7 + x)(16 + -9x) = 0Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 2
Set the factor '(16 + -9x)' equal to zero and attempt to solve: Simplifying 16 + -9x = 0 Solving 16 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -9x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -9x = 0 + -16 -9x = 0 + -16 Combine like terms: 0 + -16 = -16 -9x = -16 Divide each side by '-9'. x = 1.777777778 Simplifying x = 1.777777778Solution
x = {7, 1.777777778}
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