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Simplifying (2x + 24)(x + 7) = 90 Reorder the terms: (24 + 2x)(x + 7) = 90 Reorder the terms: (24 + 2x)(7 + x) = 90 Multiply (24 + 2x) * (7 + x) (24(7 + x) + 2x * (7 + x)) = 90 ((7 * 24 + x * 24) + 2x * (7 + x)) = 90 ((168 + 24x) + 2x * (7 + x)) = 90 (168 + 24x + (7 * 2x + x * 2x)) = 90 (168 + 24x + (14x + 2x2)) = 90 Combine like terms: 24x + 14x = 38x (168 + 38x + 2x2) = 90 Solving 168 + 38x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: 168 + -90 + 38x + 2x2 = 90 + -90 Combine like terms: 168 + -90 = 78 78 + 38x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 78 + 38x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(39 + 19x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(39 + 19x + x2)' equal to zero and attempt to solve: Simplifying 39 + 19x + x2 = 0 Solving 39 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 19x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + 19x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 19x + x2 = 0 + -39 19x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 19x + x2 = -39 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -39 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -39 + 90.25 Combine like terms: -39 + 90.25 = 51.25 90.25 + 19x + x2 = 51.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 9.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 9.5 = 7.158910532 Simplifying x + 9.5 = 7.158910532 Reorder the terms: 9.5 + x = 7.158910532 Solving 9.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 7.158910532 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 7.158910532 + -9.5 x = 7.158910532 + -9.5 Combine like terms: 7.158910532 + -9.5 = -2.341089468 x = -2.341089468 Simplifying x = -2.341089468Subproblem 2
x + 9.5 = -7.158910532 Simplifying x + 9.5 = -7.158910532 Reorder the terms: 9.5 + x = -7.158910532 Solving 9.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -7.158910532 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -7.158910532 + -9.5 x = -7.158910532 + -9.5 Combine like terms: -7.158910532 + -9.5 = -16.658910532 x = -16.658910532 Simplifying x = -16.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.341089468, -16.658910532}Solution
x = {-2.341089468, -16.658910532}
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