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Simplifying (6x + -1)(x + -5) = 8 Reorder the terms: (-1 + 6x)(x + -5) = 8 Reorder the terms: (-1 + 6x)(-5 + x) = 8 Multiply (-1 + 6x) * (-5 + x) (-1(-5 + x) + 6x * (-5 + x)) = 8 ((-5 * -1 + x * -1) + 6x * (-5 + x)) = 8 ((5 + -1x) + 6x * (-5 + x)) = 8 (5 + -1x + (-5 * 6x + x * 6x)) = 8 (5 + -1x + (-30x + 6x2)) = 8 Combine like terms: -1x + -30x = -31x (5 + -31x + 6x2) = 8 Solving 5 + -31x + 6x2 = 8 Solving for variable 'x'. Reorder the terms: 5 + -8 + -31x + 6x2 = 8 + -8 Combine like terms: 5 + -8 = -3 -3 + -31x + 6x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -3 + -31x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -5.166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5.166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5.166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5.166666667x + x2 = 0 + 0.5 -5.166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5.166666667x + x2 = 0.5 The x term is -5.166666667x. Take half its coefficient (-2.583333334). Square it (6.673611115) and add it to both sides. Add '6.673611115' to each side of the equation. -5.166666667x + 6.673611115 + x2 = 0.5 + 6.673611115 Reorder the terms: 6.673611115 + -5.166666667x + x2 = 0.5 + 6.673611115 Combine like terms: 0.5 + 6.673611115 = 7.173611115 6.673611115 + -5.166666667x + x2 = 7.173611115 Factor a perfect square on the left side: (x + -2.583333334)(x + -2.583333334) = 7.173611115 Calculate the square root of the right side: 2.678359781 Break this problem into two subproblems by setting (x + -2.583333334) equal to 2.678359781 and -2.678359781.Subproblem 1
x + -2.583333334 = 2.678359781 Simplifying x + -2.583333334 = 2.678359781 Reorder the terms: -2.583333334 + x = 2.678359781 Solving -2.583333334 + x = 2.678359781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.583333334' to each side of the equation. -2.583333334 + 2.583333334 + x = 2.678359781 + 2.583333334 Combine like terms: -2.583333334 + 2.583333334 = 0.000000000 0.000000000 + x = 2.678359781 + 2.583333334 x = 2.678359781 + 2.583333334 Combine like terms: 2.678359781 + 2.583333334 = 5.261693115 x = 5.261693115 Simplifying x = 5.261693115Subproblem 2
x + -2.583333334 = -2.678359781 Simplifying x + -2.583333334 = -2.678359781 Reorder the terms: -2.583333334 + x = -2.678359781 Solving -2.583333334 + x = -2.678359781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.583333334' to each side of the equation. -2.583333334 + 2.583333334 + x = -2.678359781 + 2.583333334 Combine like terms: -2.583333334 + 2.583333334 = 0.000000000 0.000000000 + x = -2.678359781 + 2.583333334 x = -2.678359781 + 2.583333334 Combine like terms: -2.678359781 + 2.583333334 = -0.095026447 x = -0.095026447 Simplifying x = -0.095026447Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.261693115, -0.095026447}
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