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Simplifying x2 + -1x = 115 Reorder the terms: -1x + x2 = 115 Solving -1x + x2 = 115 Solving for variable 'x'. Reorder the terms: -115 + -1x + x2 = 115 + -115 Combine like terms: 115 + -115 = 0 -115 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + -1x + 115 + x2 = 0 + 115 Reorder the terms: -115 + 115 + -1x + x2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + -1x + x2 = 0 + 115 -1x + x2 = 0 + 115 Combine like terms: 0 + 115 = 115 -1x + x2 = 115 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 115 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 115 + 0.25 Combine like terms: 115 + 0.25 = 115.25 0.25 + -1x + x2 = 115.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 115.25 Calculate the square root of the right side: 10.735455277 Break this problem into two subproblems by setting (x + -0.5) equal to 10.735455277 and -10.735455277.Subproblem 1
x + -0.5 = 10.735455277 Simplifying x + -0.5 = 10.735455277 Reorder the terms: -0.5 + x = 10.735455277 Solving -0.5 + x = 10.735455277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 10.735455277 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 10.735455277 + 0.5 x = 10.735455277 + 0.5 Combine like terms: 10.735455277 + 0.5 = 11.235455277 x = 11.235455277 Simplifying x = 11.235455277Subproblem 2
x + -0.5 = -10.735455277 Simplifying x + -0.5 = -10.735455277 Reorder the terms: -0.5 + x = -10.735455277 Solving -0.5 + x = -10.735455277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -10.735455277 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -10.735455277 + 0.5 x = -10.735455277 + 0.5 Combine like terms: -10.735455277 + 0.5 = -10.235455277 x = -10.235455277 Simplifying x = -10.235455277Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.235455277, -10.235455277}
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