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Simplifying 7 + -17x = 2x + -5x + -7x2 Combine like terms: 2x + -5x = -3x 7 + -17x = -3x + -7x2 Solving 7 + -17x = -3x + -7x2 Solving for variable 'x'. Combine like terms: -17x + 3x = -14x 7 + -14x + 7x2 = -3x + -7x2 + 3x + 7x2 Reorder the terms: 7 + -14x + 7x2 = -3x + 3x + -7x2 + 7x2 Combine like terms: -3x + 3x = 0 7 + -14x + 7x2 = 0 + -7x2 + 7x2 7 + -14x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 7 + -14x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(1 + -2x + x2) = 0 Factor a trinomial. 7((1 + -1x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {1, 1}
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