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Simplifying (3x + -2)(x + -5) = 28 Reorder the terms: (-2 + 3x)(x + -5) = 28 Reorder the terms: (-2 + 3x)(-5 + x) = 28 Multiply (-2 + 3x) * (-5 + x) (-2(-5 + x) + 3x * (-5 + x)) = 28 ((-5 * -2 + x * -2) + 3x * (-5 + x)) = 28 ((10 + -2x) + 3x * (-5 + x)) = 28 (10 + -2x + (-5 * 3x + x * 3x)) = 28 (10 + -2x + (-15x + 3x2)) = 28 Combine like terms: -2x + -15x = -17x (10 + -17x + 3x2) = 28 Solving 10 + -17x + 3x2 = 28 Solving for variable 'x'. Reorder the terms: 10 + -28 + -17x + 3x2 = 28 + -28 Combine like terms: 10 + -28 = -18 -18 + -17x + 3x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -18 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -5.666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -5.666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5.666666667x + x2 = 0 + 6 -5.666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5.666666667x + x2 = 6 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 = 6 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 6 + 8.027777782 Combine like terms: 6 + 8.027777782 = 14.027777782 8.027777782 + -5.666666667x + x2 = 14.027777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 14.027777782 Calculate the square root of the right side: 3.74536751 Break this problem into two subproblems by setting (x + -2.833333334) equal to 3.74536751 and -3.74536751.Subproblem 1
x + -2.833333334 = 3.74536751 Simplifying x + -2.833333334 = 3.74536751 Reorder the terms: -2.833333334 + x = 3.74536751 Solving -2.833333334 + x = 3.74536751 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 = 3.74536751 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.74536751 + 2.833333334 x = 3.74536751 + 2.833333334 Combine like terms: 3.74536751 + 2.833333334 = 6.578700844 x = 6.578700844 Simplifying x = 6.578700844Subproblem 2
x + -2.833333334 = -3.74536751 Simplifying x + -2.833333334 = -3.74536751 Reorder the terms: -2.833333334 + x = -3.74536751 Solving -2.833333334 + x = -3.74536751 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 = -3.74536751 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.74536751 + 2.833333334 x = -3.74536751 + 2.833333334 Combine like terms: -3.74536751 + 2.833333334 = -0.912034176 x = -0.912034176 Simplifying x = -0.912034176Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.578700844, -0.912034176}
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