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Simplifying x2 + -11x + -360 = 0 Reorder the terms: -360 + -11x + x2 = 0 Solving -360 + -11x + 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 + -11x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + -11x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -11x + x2 = 0 + 360 -11x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 -11x + x2 = 360 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 360 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 360 + 30.25 Combine like terms: 360 + 30.25 = 390.25 30.25 + -11x + x2 = 390.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 390.25 Calculate the square root of the right side: 19.754746265 Break this problem into two subproblems by setting (x + -5.5) equal to 19.754746265 and -19.754746265.Subproblem 1
x + -5.5 = 19.754746265 Simplifying x + -5.5 = 19.754746265 Reorder the terms: -5.5 + x = 19.754746265 Solving -5.5 + x = 19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 19.754746265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 19.754746265 + 5.5 x = 19.754746265 + 5.5 Combine like terms: 19.754746265 + 5.5 = 25.254746265 x = 25.254746265 Simplifying x = 25.254746265Subproblem 2
x + -5.5 = -19.754746265 Simplifying x + -5.5 = -19.754746265 Reorder the terms: -5.5 + x = -19.754746265 Solving -5.5 + x = -19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -19.754746265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -19.754746265 + 5.5 x = -19.754746265 + 5.5 Combine like terms: -19.754746265 + 5.5 = -14.254746265 x = -14.254746265 Simplifying x = -14.254746265Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.254746265, -14.254746265}
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