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Simplifying (2x + 8)(5x + 4) + (6x + -1) = 180 Reorder the terms: (8 + 2x)(5x + 4) + (6x + -1) = 180 Reorder the terms: (8 + 2x)(4 + 5x) + (6x + -1) = 180 Multiply (8 + 2x) * (4 + 5x) (8(4 + 5x) + 2x * (4 + 5x)) + (6x + -1) = 180 ((4 * 8 + 5x * 8) + 2x * (4 + 5x)) + (6x + -1) = 180 ((32 + 40x) + 2x * (4 + 5x)) + (6x + -1) = 180 (32 + 40x + (4 * 2x + 5x * 2x)) + (6x + -1) = 180 (32 + 40x + (8x + 10x2)) + (6x + -1) = 180 Combine like terms: 40x + 8x = 48x (32 + 48x + 10x2) + (6x + -1) = 180 Reorder the terms: 32 + 48x + 10x2 + (-1 + 6x) = 180 Remove parenthesis around (-1 + 6x) 32 + 48x + 10x2 + -1 + 6x = 180 Reorder the terms: 32 + -1 + 48x + 6x + 10x2 = 180 Combine like terms: 32 + -1 = 31 31 + 48x + 6x + 10x2 = 180 Combine like terms: 48x + 6x = 54x 31 + 54x + 10x2 = 180 Solving 31 + 54x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: 31 + -180 + 54x + 10x2 = 180 + -180 Combine like terms: 31 + -180 = -149 -149 + 54x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -149 + 54x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -14.9 + 5.4x + x2 = 0.0 Move the constant term to the right: Add '14.9' to each side of the equation. -14.9 + 5.4x + 14.9 + x2 = 0.0 + 14.9 Reorder the terms: -14.9 + 14.9 + 5.4x + x2 = 0.0 + 14.9 Combine like terms: -14.9 + 14.9 = 0.0 0.0 + 5.4x + x2 = 0.0 + 14.9 5.4x + x2 = 0.0 + 14.9 Combine like terms: 0.0 + 14.9 = 14.9 5.4x + x2 = 14.9 The x term is 5.4x. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4x + 7.29 + x2 = 14.9 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = 14.9 + 7.29 Combine like terms: 14.9 + 7.29 = 22.19 7.29 + 5.4x + x2 = 22.19 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 22.19 Calculate the square root of the right side: 4.710626285 Break this problem into two subproblems by setting (x + 2.7) equal to 4.710626285 and -4.710626285.Subproblem 1
x + 2.7 = 4.710626285 Simplifying x + 2.7 = 4.710626285 Reorder the terms: 2.7 + x = 4.710626285 Solving 2.7 + x = 4.710626285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 4.710626285 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 4.710626285 + -2.7 x = 4.710626285 + -2.7 Combine like terms: 4.710626285 + -2.7 = 2.010626285 x = 2.010626285 Simplifying x = 2.010626285Subproblem 2
x + 2.7 = -4.710626285 Simplifying x + 2.7 = -4.710626285 Reorder the terms: 2.7 + x = -4.710626285 Solving 2.7 + x = -4.710626285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -4.710626285 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -4.710626285 + -2.7 x = -4.710626285 + -2.7 Combine like terms: -4.710626285 + -2.7 = -7.410626285 x = -7.410626285 Simplifying x = -7.410626285Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.010626285, -7.410626285}
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