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Simplifying (18x + -9)(4x + 13) = 180 Reorder the terms: (-9 + 18x)(4x + 13) = 180 Reorder the terms: (-9 + 18x)(13 + 4x) = 180 Multiply (-9 + 18x) * (13 + 4x) (-9(13 + 4x) + 18x * (13 + 4x)) = 180 ((13 * -9 + 4x * -9) + 18x * (13 + 4x)) = 180 ((-117 + -36x) + 18x * (13 + 4x)) = 180 (-117 + -36x + (13 * 18x + 4x * 18x)) = 180 (-117 + -36x + (234x + 72x2)) = 180 Combine like terms: -36x + 234x = 198x (-117 + 198x + 72x2) = 180 Solving -117 + 198x + 72x2 = 180 Solving for variable 'x'. Reorder the terms: -117 + -180 + 198x + 72x2 = 180 + -180 Combine like terms: -117 + -180 = -297 -297 + 198x + 72x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -297 + 198x + 72x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-33 + 22x + 8x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-33 + 22x + 8x2)' equal to zero and attempt to solve: Simplifying -33 + 22x + 8x2 = 0 Solving -33 + 22x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.125 + 2.75x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + 2.75x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + 2.75x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + 2.75x + x2 = 0 + 4.125 2.75x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 2.75x + x2 = 4.125 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 4.125 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 4.125 + 1.890625 Combine like terms: 4.125 + 1.890625 = 6.015625 1.890625 + 2.75x + x2 = 6.015625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + 1.375) equal to 2.452677109 and -2.452677109.Subproblem 1
x + 1.375 = 2.452677109 Simplifying x + 1.375 = 2.452677109 Reorder the terms: 1.375 + x = 2.452677109 Solving 1.375 + x = 2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 2.452677109 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 2.452677109 + -1.375 x = 2.452677109 + -1.375 Combine like terms: 2.452677109 + -1.375 = 1.077677109 x = 1.077677109 Simplifying x = 1.077677109Subproblem 2
x + 1.375 = -2.452677109 Simplifying x + 1.375 = -2.452677109 Reorder the terms: 1.375 + x = -2.452677109 Solving 1.375 + x = -2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -2.452677109 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -2.452677109 + -1.375 x = -2.452677109 + -1.375 Combine like terms: -2.452677109 + -1.375 = -3.827677109 x = -3.827677109 Simplifying x = -3.827677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.077677109, -3.827677109}Solution
x = {1.077677109, -3.827677109}
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