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Simplifying x2 + -1x + -126 = 0 Reorder the terms: -126 + -1x + x2 = 0 Solving -126 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + -1x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + -1x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -1x + x2 = 0 + 126 -1x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 -1x + x2 = 126 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 = 126 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 126 + 0.25 Combine like terms: 126 + 0.25 = 126.25 0.25 + -1x + x2 = 126.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (x + -0.5) equal to 11.236102527 and -11.236102527.Subproblem 1
x + -0.5 = 11.236102527 Simplifying x + -0.5 = 11.236102527 Reorder the terms: -0.5 + x = 11.236102527 Solving -0.5 + x = 11.236102527 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 = 11.236102527 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 11.236102527 + 0.5 x = 11.236102527 + 0.5 Combine like terms: 11.236102527 + 0.5 = 11.736102527 x = 11.736102527 Simplifying x = 11.736102527Subproblem 2
x + -0.5 = -11.236102527 Simplifying x + -0.5 = -11.236102527 Reorder the terms: -0.5 + x = -11.236102527 Solving -0.5 + x = -11.236102527 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 = -11.236102527 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -11.236102527 + 0.5 x = -11.236102527 + 0.5 Combine like terms: -11.236102527 + 0.5 = -10.736102527 x = -10.736102527 Simplifying x = -10.736102527Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.736102527, -10.736102527}
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