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Simplifying (3x + -2)(x + -5) = 17 Reorder the terms: (-2 + 3x)(x + -5) = 17 Reorder the terms: (-2 + 3x)(-5 + x) = 17 Multiply (-2 + 3x) * (-5 + x) (-2(-5 + x) + 3x * (-5 + x)) = 17 ((-5 * -2 + x * -2) + 3x * (-5 + x)) = 17 ((10 + -2x) + 3x * (-5 + x)) = 17 (10 + -2x + (-5 * 3x + x * 3x)) = 17 (10 + -2x + (-15x + 3x2)) = 17 Combine like terms: -2x + -15x = -17x (10 + -17x + 3x2) = 17 Solving 10 + -17x + 3x2 = 17 Solving for variable 'x'. Reorder the terms: 10 + -17 + -17x + 3x2 = 17 + -17 Combine like terms: 10 + -17 = -7 -7 + -17x + 3x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -7 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -5.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -5.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -5.666666667x + x2 = 0 + 2.333333333 -5.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -5.666666667x + x2 = 2.333333333 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 = 2.333333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 2.333333333 + 8.027777782 Combine like terms: 2.333333333 + 8.027777782 = 10.361111115 8.027777782 + -5.666666667x + x2 = 10.361111115 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 10.361111115 Calculate the square root of the right side: 3.218867987 Break this problem into two subproblems by setting (x + -2.833333334) equal to 3.218867987 and -3.218867987.Subproblem 1
x + -2.833333334 = 3.218867987 Simplifying x + -2.833333334 = 3.218867987 Reorder the terms: -2.833333334 + x = 3.218867987 Solving -2.833333334 + x = 3.218867987 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 = 3.218867987 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.218867987 + 2.833333334 x = 3.218867987 + 2.833333334 Combine like terms: 3.218867987 + 2.833333334 = 6.052201321 x = 6.052201321 Simplifying x = 6.052201321Subproblem 2
x + -2.833333334 = -3.218867987 Simplifying x + -2.833333334 = -3.218867987 Reorder the terms: -2.833333334 + x = -3.218867987 Solving -2.833333334 + x = -3.218867987 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 = -3.218867987 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.218867987 + 2.833333334 x = -3.218867987 + 2.833333334 Combine like terms: -3.218867987 + 2.833333334 = -0.385534653 x = -0.385534653 Simplifying x = -0.385534653Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.052201321, -0.385534653}
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