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Simplifying (3x + 2)(x + -1) + -13 = 2x(8 + -1x) Reorder the terms: (2 + 3x)(x + -1) + -13 = 2x(8 + -1x) Reorder the terms: (2 + 3x)(-1 + x) + -13 = 2x(8 + -1x) Multiply (2 + 3x) * (-1 + x) (2(-1 + x) + 3x * (-1 + x)) + -13 = 2x(8 + -1x) ((-1 * 2 + x * 2) + 3x * (-1 + x)) + -13 = 2x(8 + -1x) ((-2 + 2x) + 3x * (-1 + x)) + -13 = 2x(8 + -1x) (-2 + 2x + (-1 * 3x + x * 3x)) + -13 = 2x(8 + -1x) (-2 + 2x + (-3x + 3x2)) + -13 = 2x(8 + -1x) Combine like terms: 2x + -3x = -1x (-2 + -1x + 3x2) + -13 = 2x(8 + -1x) Reorder the terms: -2 + -13 + -1x + 3x2 = 2x(8 + -1x) Combine like terms: -2 + -13 = -15 -15 + -1x + 3x2 = 2x(8 + -1x) -15 + -1x + 3x2 = (8 * 2x + -1x * 2x) -15 + -1x + 3x2 = (16x + -2x2) Solving -15 + -1x + 3x2 = 16x + -2x2 Solving for variable 'x'. Reorder the terms: -15 + -1x + -16x + 3x2 + 2x2 = 16x + -2x2 + -16x + 2x2 Combine like terms: -1x + -16x = -17x -15 + -17x + 3x2 + 2x2 = 16x + -2x2 + -16x + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 -15 + -17x + 5x2 = 16x + -2x2 + -16x + 2x2 Reorder the terms: -15 + -17x + 5x2 = 16x + -16x + -2x2 + 2x2 Combine like terms: 16x + -16x = 0 -15 + -17x + 5x2 = 0 + -2x2 + 2x2 -15 + -17x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -15 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + -3.4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -3.4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.4x + x2 = 0 + 3 -3.4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.4x + x2 = 3 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 3 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 3 + 2.89 Combine like terms: 3 + 2.89 = 5.89 2.89 + -3.4x + x2 = 5.89 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 5.89 Calculate the square root of the right side: 2.42693222 Break this problem into two subproblems by setting (x + -1.7) equal to 2.42693222 and -2.42693222.Subproblem 1
x + -1.7 = 2.42693222 Simplifying x + -1.7 = 2.42693222 Reorder the terms: -1.7 + x = 2.42693222 Solving -1.7 + x = 2.42693222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 2.42693222 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.42693222 + 1.7 x = 2.42693222 + 1.7 Combine like terms: 2.42693222 + 1.7 = 4.12693222 x = 4.12693222 Simplifying x = 4.12693222Subproblem 2
x + -1.7 = -2.42693222 Simplifying x + -1.7 = -2.42693222 Reorder the terms: -1.7 + x = -2.42693222 Solving -1.7 + x = -2.42693222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -2.42693222 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.42693222 + 1.7 x = -2.42693222 + 1.7 Combine like terms: -2.42693222 + 1.7 = -0.72693222 x = -0.72693222 Simplifying x = -0.72693222Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.12693222, -0.72693222}
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