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Simplifying x2 + -1x + -216 = 0 Reorder the terms: -216 + -1x + x2 = 0 Solving -216 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + -1x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + -1x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + -1x + x2 = 0 + 216 -1x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 -1x + x2 = 216 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 = 216 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 216 + 0.25 Combine like terms: 216 + 0.25 = 216.25 0.25 + -1x + x2 = 216.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 216.25 Calculate the square root of the right side: 14.70544117 Break this problem into two subproblems by setting (x + -0.5) equal to 14.70544117 and -14.70544117.Subproblem 1
x + -0.5 = 14.70544117 Simplifying x + -0.5 = 14.70544117 Reorder the terms: -0.5 + x = 14.70544117 Solving -0.5 + x = 14.70544117 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 = 14.70544117 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 14.70544117 + 0.5 x = 14.70544117 + 0.5 Combine like terms: 14.70544117 + 0.5 = 15.20544117 x = 15.20544117 Simplifying x = 15.20544117Subproblem 2
x + -0.5 = -14.70544117 Simplifying x + -0.5 = -14.70544117 Reorder the terms: -0.5 + x = -14.70544117 Solving -0.5 + x = -14.70544117 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 = -14.70544117 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -14.70544117 + 0.5 x = -14.70544117 + 0.5 Combine like terms: -14.70544117 + 0.5 = -14.20544117 x = -14.20544117 Simplifying x = -14.20544117Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.20544117, -14.20544117}
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