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Simplifying 7x2 + 6x = 17x + -5x2 Reorder the terms: 6x + 7x2 = 17x + -5x2 Solving 6x + 7x2 = 17x + -5x2 Solving for variable 'x'. Reorder the terms: 6x + -17x + 7x2 + 5x2 = 17x + -5x2 + -17x + 5x2 Combine like terms: 6x + -17x = -11x -11x + 7x2 + 5x2 = 17x + -5x2 + -17x + 5x2 Combine like terms: 7x2 + 5x2 = 12x2 -11x + 12x2 = 17x + -5x2 + -17x + 5x2 Reorder the terms: -11x + 12x2 = 17x + -17x + -5x2 + 5x2 Combine like terms: 17x + -17x = 0 -11x + 12x2 = 0 + -5x2 + 5x2 -11x + 12x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -11x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 12x) = 0Subproblem 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 '(-11 + 12x)' equal to zero and attempt to solve: Simplifying -11 + 12x = 0 Solving -11 + 12x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 12x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 12x = 0 + 11 12x = 0 + 11 Combine like terms: 0 + 11 = 11 12x = 11 Divide each side by '12'. x = 0.9166666667 Simplifying x = 0.9166666667Solution
x = {0, 0.9166666667}
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