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Simplifying (x + 8)(x + 5) = 50 Reorder the terms: (8 + x)(x + 5) = 50 Reorder the terms: (8 + x)(5 + x) = 50 Multiply (8 + x) * (5 + x) (8(5 + x) + x(5 + x)) = 50 ((5 * 8 + x * 8) + x(5 + x)) = 50 ((40 + 8x) + x(5 + x)) = 50 (40 + 8x + (5 * x + x * x)) = 50 (40 + 8x + (5x + x2)) = 50 Combine like terms: 8x + 5x = 13x (40 + 13x + x2) = 50 Solving 40 + 13x + x2 = 50 Solving for variable 'x'. Reorder the terms: 40 + -50 + 13x + x2 = 50 + -50 Combine like terms: 40 + -50 = -10 -10 + 13x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -10 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 13x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 13x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 13x + x2 = 0 + 10 13x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 13x + x2 = 10 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 10 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 10 + 42.25 Combine like terms: 10 + 42.25 = 52.25 42.25 + 13x + x2 = 52.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 6.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 6.5 = 7.228416147 Simplifying x + 6.5 = 7.228416147 Reorder the terms: 6.5 + x = 7.228416147 Solving 6.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.228416147 + -6.5 x = 7.228416147 + -6.5 Combine like terms: 7.228416147 + -6.5 = 0.728416147 x = 0.728416147 Simplifying x = 0.728416147Subproblem 2
x + 6.5 = -7.228416147 Simplifying x + 6.5 = -7.228416147 Reorder the terms: 6.5 + x = -7.228416147 Solving 6.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.228416147 + -6.5 x = -7.228416147 + -6.5 Combine like terms: -7.228416147 + -6.5 = -13.728416147 x = -13.728416147 Simplifying x = -13.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.728416147, -13.728416147}
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