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Simplifying (3x + -8)(6x + -41) = 180 Reorder the terms: (-8 + 3x)(6x + -41) = 180 Reorder the terms: (-8 + 3x)(-41 + 6x) = 180 Multiply (-8 + 3x) * (-41 + 6x) (-8(-41 + 6x) + 3x * (-41 + 6x)) = 180 ((-41 * -8 + 6x * -8) + 3x * (-41 + 6x)) = 180 ((328 + -48x) + 3x * (-41 + 6x)) = 180 (328 + -48x + (-41 * 3x + 6x * 3x)) = 180 (328 + -48x + (-123x + 18x2)) = 180 Combine like terms: -48x + -123x = -171x (328 + -171x + 18x2) = 180 Solving 328 + -171x + 18x2 = 180 Solving for variable 'x'. Reorder the terms: 328 + -180 + -171x + 18x2 = 180 + -180 Combine like terms: 328 + -180 = 148 148 + -171x + 18x2 = 180 + -180 Combine like terms: 180 + -180 = 0 148 + -171x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 8.222222222 + -9.5x + x2 = 0 Move the constant term to the right: Add '-8.222222222' to each side of the equation. 8.222222222 + -9.5x + -8.222222222 + x2 = 0 + -8.222222222 Reorder the terms: 8.222222222 + -8.222222222 + -9.5x + x2 = 0 + -8.222222222 Combine like terms: 8.222222222 + -8.222222222 = 0.000000000 0.000000000 + -9.5x + x2 = 0 + -8.222222222 -9.5x + x2 = 0 + -8.222222222 Combine like terms: 0 + -8.222222222 = -8.222222222 -9.5x + x2 = -8.222222222 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -8.222222222 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -8.222222222 + 22.5625 Combine like terms: -8.222222222 + 22.5625 = 14.340277778 22.5625 + -9.5x + x2 = 14.340277778 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 14.340277778 Calculate the square root of the right side: 3.786855923 Break this problem into two subproblems by setting (x + -4.75) equal to 3.786855923 and -3.786855923.Subproblem 1
x + -4.75 = 3.786855923 Simplifying x + -4.75 = 3.786855923 Reorder the terms: -4.75 + x = 3.786855923 Solving -4.75 + x = 3.786855923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 3.786855923 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 3.786855923 + 4.75 x = 3.786855923 + 4.75 Combine like terms: 3.786855923 + 4.75 = 8.536855923 x = 8.536855923 Simplifying x = 8.536855923Subproblem 2
x + -4.75 = -3.786855923 Simplifying x + -4.75 = -3.786855923 Reorder the terms: -4.75 + x = -3.786855923 Solving -4.75 + x = -3.786855923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -3.786855923 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -3.786855923 + 4.75 x = -3.786855923 + 4.75 Combine like terms: -3.786855923 + 4.75 = 0.963144077 x = 0.963144077 Simplifying x = 0.963144077Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.536855923, 0.963144077}
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