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Simplifying 41x2 + -41x = -15x2 + 7 Reorder the terms: -41x + 41x2 = -15x2 + 7 Reorder the terms: -41x + 41x2 = 7 + -15x2 Solving -41x + 41x2 = 7 + -15x2 Solving for variable 'x'. Reorder the terms: -7 + -41x + 41x2 + 15x2 = 7 + -15x2 + -7 + 15x2 Combine like terms: 41x2 + 15x2 = 56x2 -7 + -41x + 56x2 = 7 + -15x2 + -7 + 15x2 Reorder the terms: -7 + -41x + 56x2 = 7 + -7 + -15x2 + 15x2 Combine like terms: 7 + -7 = 0 -7 + -41x + 56x2 = 0 + -15x2 + 15x2 -7 + -41x + 56x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 -7 + -41x + 56x2 = 0 Factor a trinomial. (-1 + -7x)(7 + -8x) = 0Subproblem 1
Set the factor '(-1 + -7x)' equal to zero and attempt to solve: Simplifying -1 + -7x = 0 Solving -1 + -7x = 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 + -7x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7x = 0 + 1 -7x = 0 + 1 Combine like terms: 0 + 1 = 1 -7x = 1 Divide each side by '-7'. x = -0.1428571429 Simplifying x = -0.1428571429Subproblem 2
Set the factor '(7 + -8x)' equal to zero and attempt to solve: Simplifying 7 + -8x = 0 Solving 7 + -8x = 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 + -8x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8x = 0 + -7 -8x = 0 + -7 Combine like terms: 0 + -7 = -7 -8x = -7 Divide each side by '-8'. x = 0.875 Simplifying x = 0.875Solution
x = {-0.1428571429, 0.875}
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