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Simplifying x2 + 13x + -29 = 0 Reorder the terms: -29 + 13x + x2 = 0 Solving -29 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 13x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 13x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 13x + x2 = 0 + 29 13x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 13x + x2 = 29 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 = 29 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 29 + 42.25 Combine like terms: 29 + 42.25 = 71.25 42.25 + 13x + x2 = 71.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (x + 6.5) equal to 8.440971508 and -8.440971508.Subproblem 1
x + 6.5 = 8.440971508 Simplifying x + 6.5 = 8.440971508 Reorder the terms: 6.5 + x = 8.440971508 Solving 6.5 + x = 8.440971508 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 = 8.440971508 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.440971508 + -6.5 x = 8.440971508 + -6.5 Combine like terms: 8.440971508 + -6.5 = 1.940971508 x = 1.940971508 Simplifying x = 1.940971508Subproblem 2
x + 6.5 = -8.440971508 Simplifying x + 6.5 = -8.440971508 Reorder the terms: 6.5 + x = -8.440971508 Solving 6.5 + x = -8.440971508 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 = -8.440971508 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.440971508 + -6.5 x = -8.440971508 + -6.5 Combine like terms: -8.440971508 + -6.5 = -14.940971508 x = -14.940971508 Simplifying x = -14.940971508Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.940971508, -14.940971508}
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