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Simplifying (2x + 6)(x + 8) = 780 Reorder the terms: (6 + 2x)(x + 8) = 780 Reorder the terms: (6 + 2x)(8 + x) = 780 Multiply (6 + 2x) * (8 + x) (6(8 + x) + 2x * (8 + x)) = 780 ((8 * 6 + x * 6) + 2x * (8 + x)) = 780 ((48 + 6x) + 2x * (8 + x)) = 780 (48 + 6x + (8 * 2x + x * 2x)) = 780 (48 + 6x + (16x + 2x2)) = 780 Combine like terms: 6x + 16x = 22x (48 + 22x + 2x2) = 780 Solving 48 + 22x + 2x2 = 780 Solving for variable 'x'. Reorder the terms: 48 + -780 + 22x + 2x2 = 780 + -780 Combine like terms: 48 + -780 = -732 -732 + 22x + 2x2 = 780 + -780 Combine like terms: 780 + -780 = 0 -732 + 22x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-366 + 11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-366 + 11x + x2)' equal to zero and attempt to solve: Simplifying -366 + 11x + x2 = 0 Solving -366 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '366' to each side of the equation. -366 + 11x + 366 + x2 = 0 + 366 Reorder the terms: -366 + 366 + 11x + x2 = 0 + 366 Combine like terms: -366 + 366 = 0 0 + 11x + x2 = 0 + 366 11x + x2 = 0 + 366 Combine like terms: 0 + 366 = 366 11x + x2 = 366 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 366 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 366 + 30.25 Combine like terms: 366 + 30.25 = 396.25 30.25 + 11x + x2 = 396.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 396.25 Calculate the square root of the right side: 19.906029237 Break this problem into two subproblems by setting (x + 5.5) equal to 19.906029237 and -19.906029237.Subproblem 1
x + 5.5 = 19.906029237 Simplifying x + 5.5 = 19.906029237 Reorder the terms: 5.5 + x = 19.906029237 Solving 5.5 + x = 19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 19.906029237 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 19.906029237 + -5.5 x = 19.906029237 + -5.5 Combine like terms: 19.906029237 + -5.5 = 14.406029237 x = 14.406029237 Simplifying x = 14.406029237Subproblem 2
x + 5.5 = -19.906029237 Simplifying x + 5.5 = -19.906029237 Reorder the terms: 5.5 + x = -19.906029237 Solving 5.5 + x = -19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -19.906029237 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -19.906029237 + -5.5 x = -19.906029237 + -5.5 Combine like terms: -19.906029237 + -5.5 = -25.406029237 x = -25.406029237 Simplifying x = -25.406029237Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.406029237, -25.406029237}Solution
x = {14.406029237, -25.406029237}
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