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Simplifying 7x2 + -42 = 3x2 + -17x Reorder the terms: -42 + 7x2 = 3x2 + -17x Reorder the terms: -42 + 7x2 = -17x + 3x2 Solving -42 + 7x2 = -17x + 3x2 Solving for variable 'x'. Reorder the terms: -42 + 17x + 7x2 + -3x2 = -17x + 3x2 + 17x + -3x2 Combine like terms: 7x2 + -3x2 = 4x2 -42 + 17x + 4x2 = -17x + 3x2 + 17x + -3x2 Reorder the terms: -42 + 17x + 4x2 = -17x + 17x + 3x2 + -3x2 Combine like terms: -17x + 17x = 0 -42 + 17x + 4x2 = 0 + 3x2 + -3x2 -42 + 17x + 4x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -42 + 17x + 4x2 = 0 Factor a trinomial. (-6 + -1x)(7 + -4x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Solution
x = {-6, 1.75}
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