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Simplifying (5x + 1)(x + 3) + -8 = 5(x + 5) Reorder the terms: (1 + 5x)(x + 3) + -8 = 5(x + 5) Reorder the terms: (1 + 5x)(3 + x) + -8 = 5(x + 5) Multiply (1 + 5x) * (3 + x) (1(3 + x) + 5x * (3 + x)) + -8 = 5(x + 5) ((3 * 1 + x * 1) + 5x * (3 + x)) + -8 = 5(x + 5) ((3 + 1x) + 5x * (3 + x)) + -8 = 5(x + 5) (3 + 1x + (3 * 5x + x * 5x)) + -8 = 5(x + 5) (3 + 1x + (15x + 5x2)) + -8 = 5(x + 5) Combine like terms: 1x + 15x = 16x (3 + 16x + 5x2) + -8 = 5(x + 5) Reorder the terms: 3 + -8 + 16x + 5x2 = 5(x + 5) Combine like terms: 3 + -8 = -5 -5 + 16x + 5x2 = 5(x + 5) Reorder the terms: -5 + 16x + 5x2 = 5(5 + x) -5 + 16x + 5x2 = (5 * 5 + x * 5) -5 + 16x + 5x2 = (25 + 5x) Solving -5 + 16x + 5x2 = 25 + 5x Solving for variable 'x'. Reorder the terms: -5 + -25 + 16x + -5x + 5x2 = 25 + 5x + -25 + -5x Combine like terms: -5 + -25 = -30 -30 + 16x + -5x + 5x2 = 25 + 5x + -25 + -5x Combine like terms: 16x + -5x = 11x -30 + 11x + 5x2 = 25 + 5x + -25 + -5x Reorder the terms: -30 + 11x + 5x2 = 25 + -25 + 5x + -5x Combine like terms: 25 + -25 = 0 -30 + 11x + 5x2 = 0 + 5x + -5x -30 + 11x + 5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -30 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + 2.2x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 2.2x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 2.2x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2.2x + x2 = 0 + 6 2.2x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 2.2x + x2 = 6 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 6 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 6 + 1.21 Combine like terms: 6 + 1.21 = 7.21 1.21 + 2.2x + x2 = 7.21 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 7.21 Calculate the square root of the right side: 2.685144316 Break this problem into two subproblems by setting (x + 1.1) equal to 2.685144316 and -2.685144316.Subproblem 1
x + 1.1 = 2.685144316 Simplifying x + 1.1 = 2.685144316 Reorder the terms: 1.1 + x = 2.685144316 Solving 1.1 + x = 2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 2.685144316 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.685144316 + -1.1 x = 2.685144316 + -1.1 Combine like terms: 2.685144316 + -1.1 = 1.585144316 x = 1.585144316 Simplifying x = 1.585144316Subproblem 2
x + 1.1 = -2.685144316 Simplifying x + 1.1 = -2.685144316 Reorder the terms: 1.1 + x = -2.685144316 Solving 1.1 + x = -2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -2.685144316 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.685144316 + -1.1 x = -2.685144316 + -1.1 Combine like terms: -2.685144316 + -1.1 = -3.785144316 x = -3.785144316 Simplifying x = -3.785144316Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.585144316, -3.785144316}
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