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Simplifying x2 + -1x + -360 = 0 Reorder the terms: -360 + -1x + x2 = 0 Solving -360 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + -1x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + -1x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -1x + x2 = 0 + 360 -1x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 -1x + x2 = 360 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 = 360 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 360 + 0.25 Combine like terms: 360 + 0.25 = 360.25 0.25 + -1x + x2 = 360.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 360.25 Calculate the square root of the right side: 18.980252896 Break this problem into two subproblems by setting (x + -0.5) equal to 18.980252896 and -18.980252896.Subproblem 1
x + -0.5 = 18.980252896 Simplifying x + -0.5 = 18.980252896 Reorder the terms: -0.5 + x = 18.980252896 Solving -0.5 + x = 18.980252896 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 = 18.980252896 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 18.980252896 + 0.5 x = 18.980252896 + 0.5 Combine like terms: 18.980252896 + 0.5 = 19.480252896 x = 19.480252896 Simplifying x = 19.480252896Subproblem 2
x + -0.5 = -18.980252896 Simplifying x + -0.5 = -18.980252896 Reorder the terms: -0.5 + x = -18.980252896 Solving -0.5 + x = -18.980252896 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 = -18.980252896 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -18.980252896 + 0.5 x = -18.980252896 + 0.5 Combine like terms: -18.980252896 + 0.5 = -18.480252896 x = -18.480252896 Simplifying x = -18.480252896Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.480252896, -18.480252896}
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