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Simplifying x2 + 12x + -216 = 0 Reorder the terms: -216 + 12x + x2 = 0 Solving -216 + 12x + 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 + 12x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 12x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 12x + x2 = 0 + 216 12x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 12x + x2 = 216 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 216 + 36 Reorder the terms: 36 + 12x + x2 = 216 + 36 Combine like terms: 216 + 36 = 252 36 + 12x + x2 = 252 Factor a perfect square on the left side: (x + 6)(x + 6) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + 6) equal to 15.874507866 and -15.874507866.Subproblem 1
x + 6 = 15.874507866 Simplifying x + 6 = 15.874507866 Reorder the terms: 6 + x = 15.874507866 Solving 6 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 15.874507866 + -6 Combine like terms: 6 + -6 = 0 0 + x = 15.874507866 + -6 x = 15.874507866 + -6 Combine like terms: 15.874507866 + -6 = 9.874507866 x = 9.874507866 Simplifying x = 9.874507866Subproblem 2
x + 6 = -15.874507866 Simplifying x + 6 = -15.874507866 Reorder the terms: 6 + x = -15.874507866 Solving 6 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -15.874507866 + -6 Combine like terms: 6 + -6 = 0 0 + x = -15.874507866 + -6 x = -15.874507866 + -6 Combine like terms: -15.874507866 + -6 = -21.874507866 x = -21.874507866 Simplifying x = -21.874507866Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.874507866, -21.874507866}
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