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Simplifying (x + 8)(x + 3) = 119 Reorder the terms: (8 + x)(x + 3) = 119 Reorder the terms: (8 + x)(3 + x) = 119 Multiply (8 + x) * (3 + x) (8(3 + x) + x(3 + x)) = 119 ((3 * 8 + x * 8) + x(3 + x)) = 119 ((24 + 8x) + x(3 + x)) = 119 (24 + 8x + (3 * x + x * x)) = 119 (24 + 8x + (3x + x2)) = 119 Combine like terms: 8x + 3x = 11x (24 + 11x + x2) = 119 Solving 24 + 11x + x2 = 119 Solving for variable 'x'. Reorder the terms: 24 + -119 + 11x + x2 = 119 + -119 Combine like terms: 24 + -119 = -95 -95 + 11x + x2 = 119 + -119 Combine like terms: 119 + -119 = 0 -95 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + 11x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 11x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 11x + x2 = 0 + 95 11x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 11x + x2 = 95 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 = 95 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 95 + 30.25 Combine like terms: 95 + 30.25 = 125.25 30.25 + 11x + x2 = 125.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 125.25 Calculate the square root of the right side: 11.191514643 Break this problem into two subproblems by setting (x + 5.5) equal to 11.191514643 and -11.191514643.Subproblem 1
x + 5.5 = 11.191514643 Simplifying x + 5.5 = 11.191514643 Reorder the terms: 5.5 + x = 11.191514643 Solving 5.5 + x = 11.191514643 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 = 11.191514643 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 11.191514643 + -5.5 x = 11.191514643 + -5.5 Combine like terms: 11.191514643 + -5.5 = 5.691514643 x = 5.691514643 Simplifying x = 5.691514643Subproblem 2
x + 5.5 = -11.191514643 Simplifying x + 5.5 = -11.191514643 Reorder the terms: 5.5 + x = -11.191514643 Solving 5.5 + x = -11.191514643 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 = -11.191514643 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -11.191514643 + -5.5 x = -11.191514643 + -5.5 Combine like terms: -11.191514643 + -5.5 = -16.691514643 x = -16.691514643 Simplifying x = -16.691514643Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.691514643, -16.691514643}
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