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Simplifying x2 + -1x + -516 = 0 Reorder the terms: -516 + -1x + x2 = 0 Solving -516 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '516' to each side of the equation. -516 + -1x + 516 + x2 = 0 + 516 Reorder the terms: -516 + 516 + -1x + x2 = 0 + 516 Combine like terms: -516 + 516 = 0 0 + -1x + x2 = 0 + 516 -1x + x2 = 0 + 516 Combine like terms: 0 + 516 = 516 -1x + x2 = 516 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 = 516 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 516 + 0.25 Combine like terms: 516 + 0.25 = 516.25 0.25 + -1x + x2 = 516.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 516.25 Calculate the square root of the right side: 22.721135535 Break this problem into two subproblems by setting (x + -0.5) equal to 22.721135535 and -22.721135535.Subproblem 1
x + -0.5 = 22.721135535 Simplifying x + -0.5 = 22.721135535 Reorder the terms: -0.5 + x = 22.721135535 Solving -0.5 + x = 22.721135535 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 = 22.721135535 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 22.721135535 + 0.5 x = 22.721135535 + 0.5 Combine like terms: 22.721135535 + 0.5 = 23.221135535 x = 23.221135535 Simplifying x = 23.221135535Subproblem 2
x + -0.5 = -22.721135535 Simplifying x + -0.5 = -22.721135535 Reorder the terms: -0.5 + x = -22.721135535 Solving -0.5 + x = -22.721135535 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 = -22.721135535 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -22.721135535 + 0.5 x = -22.721135535 + 0.5 Combine like terms: -22.721135535 + 0.5 = -22.221135535 x = -22.221135535 Simplifying x = -22.221135535Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.221135535, -22.221135535}
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