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Simplifying x2 + 13x + -255 = 0 Reorder the terms: -255 + 13x + x2 = 0 Solving -255 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '255' to each side of the equation. -255 + 13x + 255 + x2 = 0 + 255 Reorder the terms: -255 + 255 + 13x + x2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + 13x + x2 = 0 + 255 13x + x2 = 0 + 255 Combine like terms: 0 + 255 = 255 13x + x2 = 255 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 = 255 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 255 + 42.25 Combine like terms: 255 + 42.25 = 297.25 42.25 + 13x + x2 = 297.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 297.25 Calculate the square root of the right side: 17.24093965 Break this problem into two subproblems by setting (x + 6.5) equal to 17.24093965 and -17.24093965.Subproblem 1
x + 6.5 = 17.24093965 Simplifying x + 6.5 = 17.24093965 Reorder the terms: 6.5 + x = 17.24093965 Solving 6.5 + x = 17.24093965 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 = 17.24093965 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 17.24093965 + -6.5 x = 17.24093965 + -6.5 Combine like terms: 17.24093965 + -6.5 = 10.74093965 x = 10.74093965 Simplifying x = 10.74093965Subproblem 2
x + 6.5 = -17.24093965 Simplifying x + 6.5 = -17.24093965 Reorder the terms: 6.5 + x = -17.24093965 Solving 6.5 + x = -17.24093965 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 = -17.24093965 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -17.24093965 + -6.5 x = -17.24093965 + -6.5 Combine like terms: -17.24093965 + -6.5 = -23.74093965 x = -23.74093965 Simplifying x = -23.74093965Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.74093965, -23.74093965}
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