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Simplifying (3x + -8)(x + -3) = 15 Reorder the terms: (-8 + 3x)(x + -3) = 15 Reorder the terms: (-8 + 3x)(-3 + x) = 15 Multiply (-8 + 3x) * (-3 + x) (-8(-3 + x) + 3x * (-3 + x)) = 15 ((-3 * -8 + x * -8) + 3x * (-3 + x)) = 15 ((24 + -8x) + 3x * (-3 + x)) = 15 (24 + -8x + (-3 * 3x + x * 3x)) = 15 (24 + -8x + (-9x + 3x2)) = 15 Combine like terms: -8x + -9x = -17x (24 + -17x + 3x2) = 15 Solving 24 + -17x + 3x2 = 15 Solving for variable 'x'. Reorder the terms: 24 + -15 + -17x + 3x2 = 15 + -15 Combine like terms: 24 + -15 = 9 9 + -17x + 3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 9 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.666666667x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -5.666666667x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.666666667x + x2 = 0 + -3 -5.666666667x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.666666667x + x2 = -3 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = -3 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = -3 + 8.027777782 Combine like terms: -3 + 8.027777782 = 5.027777782 8.027777782 + -5.666666667x + x2 = 5.027777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 5.027777782 Calculate the square root of the right side: 2.242270675 Break this problem into two subproblems by setting (x + -2.833333334) equal to 2.242270675 and -2.242270675.Subproblem 1
x + -2.833333334 = 2.242270675 Simplifying x + -2.833333334 = 2.242270675 Reorder the terms: -2.833333334 + x = 2.242270675 Solving -2.833333334 + x = 2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 2.242270675 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 2.242270675 + 2.833333334 x = 2.242270675 + 2.833333334 Combine like terms: 2.242270675 + 2.833333334 = 5.075604009 x = 5.075604009 Simplifying x = 5.075604009Subproblem 2
x + -2.833333334 = -2.242270675 Simplifying x + -2.833333334 = -2.242270675 Reorder the terms: -2.833333334 + x = -2.242270675 Solving -2.833333334 + x = -2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -2.242270675 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -2.242270675 + 2.833333334 x = -2.242270675 + 2.833333334 Combine like terms: -2.242270675 + 2.833333334 = 0.591062659 x = 0.591062659 Simplifying x = 0.591062659Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.075604009, 0.591062659}
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