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Simplifying (5x + 9)(x + -10) = -17x + -106 Reorder the terms: (9 + 5x)(x + -10) = -17x + -106 Reorder the terms: (9 + 5x)(-10 + x) = -17x + -106 Multiply (9 + 5x) * (-10 + x) (9(-10 + x) + 5x * (-10 + x)) = -17x + -106 ((-10 * 9 + x * 9) + 5x * (-10 + x)) = -17x + -106 ((-90 + 9x) + 5x * (-10 + x)) = -17x + -106 (-90 + 9x + (-10 * 5x + x * 5x)) = -17x + -106 (-90 + 9x + (-50x + 5x2)) = -17x + -106 Combine like terms: 9x + -50x = -41x (-90 + -41x + 5x2) = -17x + -106 Reorder the terms: -90 + -41x + 5x2 = -106 + -17x Solving -90 + -41x + 5x2 = -106 + -17x Solving for variable 'x'. Reorder the terms: -90 + 106 + -41x + 17x + 5x2 = -106 + -17x + 106 + 17x Combine like terms: -90 + 106 = 16 16 + -41x + 17x + 5x2 = -106 + -17x + 106 + 17x Combine like terms: -41x + 17x = -24x 16 + -24x + 5x2 = -106 + -17x + 106 + 17x Reorder the terms: 16 + -24x + 5x2 = -106 + 106 + -17x + 17x Combine like terms: -106 + 106 = 0 16 + -24x + 5x2 = 0 + -17x + 17x 16 + -24x + 5x2 = -17x + 17x Combine like terms: -17x + 17x = 0 16 + -24x + 5x2 = 0 Factor a trinomial. (4 + -5x)(4 + -1x) = 0Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0.8, 4}
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