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Simplifying x2 + 13x + -176 = 0 Reorder the terms: -176 + 13x + x2 = 0 Solving -176 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '176' to each side of the equation. -176 + 13x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + 13x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + 13x + x2 = 0 + 176 13x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 13x + x2 = 176 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 = 176 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 176 + 42.25 Combine like terms: 176 + 42.25 = 218.25 42.25 + 13x + x2 = 218.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 218.25 Calculate the square root of the right side: 14.773286703 Break this problem into two subproblems by setting (x + 6.5) equal to 14.773286703 and -14.773286703.Subproblem 1
x + 6.5 = 14.773286703 Simplifying x + 6.5 = 14.773286703 Reorder the terms: 6.5 + x = 14.773286703 Solving 6.5 + x = 14.773286703 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 = 14.773286703 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 14.773286703 + -6.5 x = 14.773286703 + -6.5 Combine like terms: 14.773286703 + -6.5 = 8.273286703 x = 8.273286703 Simplifying x = 8.273286703Subproblem 2
x + 6.5 = -14.773286703 Simplifying x + 6.5 = -14.773286703 Reorder the terms: 6.5 + x = -14.773286703 Solving 6.5 + x = -14.773286703 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 = -14.773286703 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -14.773286703 + -6.5 x = -14.773286703 + -6.5 Combine like terms: -14.773286703 + -6.5 = -21.273286703 x = -21.273286703 Simplifying x = -21.273286703Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.273286703, -21.273286703}
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