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Simplifying x2 + -1x + -66 = 0 Reorder the terms: -66 + -1x + x2 = 0 Solving -66 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + -1x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + -1x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + -1x + x2 = 0 + 66 -1x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 -1x + x2 = 66 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 = 66 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 66 + 0.25 Combine like terms: 66 + 0.25 = 66.25 0.25 + -1x + x2 = 66.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + -0.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + -0.5 = 8.139410298 Simplifying x + -0.5 = 8.139410298 Reorder the terms: -0.5 + x = 8.139410298 Solving -0.5 + x = 8.139410298 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 = 8.139410298 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.139410298 + 0.5 x = 8.139410298 + 0.5 Combine like terms: 8.139410298 + 0.5 = 8.639410298 x = 8.639410298 Simplifying x = 8.639410298Subproblem 2
x + -0.5 = -8.139410298 Simplifying x + -0.5 = -8.139410298 Reorder the terms: -0.5 + x = -8.139410298 Solving -0.5 + x = -8.139410298 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 = -8.139410298 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.139410298 + 0.5 x = -8.139410298 + 0.5 Combine like terms: -8.139410298 + 0.5 = -7.639410298 x = -7.639410298 Simplifying x = -7.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.639410298, -7.639410298}
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