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Simplifying x * x + 2x + -216 = 0 Multiply x * x x2 + 2x + -216 = 0 Reorder the terms: -216 + 2x + x2 = 0 Solving -216 + 2x + 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 + 2x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 2x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 2x + x2 = 0 + 216 2x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 2x + x2 = 216 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 216 + 1 Reorder the terms: 1 + 2x + x2 = 216 + 1 Combine like terms: 216 + 1 = 217 1 + 2x + x2 = 217 Factor a perfect square on the left side: (x + 1)(x + 1) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + 1) equal to 14.730919863 and -14.730919863.Subproblem 1
x + 1 = 14.730919863 Simplifying x + 1 = 14.730919863 Reorder the terms: 1 + x = 14.730919863 Solving 1 + x = 14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 14.730919863 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.730919863 + -1 x = 14.730919863 + -1 Combine like terms: 14.730919863 + -1 = 13.730919863 x = 13.730919863 Simplifying x = 13.730919863Subproblem 2
x + 1 = -14.730919863 Simplifying x + 1 = -14.730919863 Reorder the terms: 1 + x = -14.730919863 Solving 1 + x = -14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -14.730919863 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.730919863 + -1 x = -14.730919863 + -1 Combine like terms: -14.730919863 + -1 = -15.730919863 x = -15.730919863 Simplifying x = -15.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.730919863, -15.730919863}
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