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Simplifying 0 = 6x2 + -17x + 10 Reorder the terms: 0 = 10 + -17x + 6x2 Solving 0 = 10 + -17x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + 17x + -6x2 = 10 + -17x + 6x2 + -10 + 17x + -6x2 Reorder the terms: -10 + 17x + -6x2 = 10 + -10 + -17x + 17x + 6x2 + -6x2 Combine like terms: 10 + -10 = 0 -10 + 17x + -6x2 = 0 + -17x + 17x + 6x2 + -6x2 -10 + 17x + -6x2 = -17x + 17x + 6x2 + -6x2 Combine like terms: -17x + 17x = 0 -10 + 17x + -6x2 = 0 + 6x2 + -6x2 -10 + 17x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -10 + 17x + -6x2 = 0 Factor a trinomial. (-2 + x)(5 + -6x) = 0Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {2, 0.8333333333}
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