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Simplifying x2 + -24x + -108 = 0 Reorder the terms: -108 + -24x + x2 = 0 Solving -108 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -24x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -24x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -24x + x2 = 0 + 108 -24x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -24x + x2 = 108 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 108 + 144 Reorder the terms: 144 + -24x + x2 = 108 + 144 Combine like terms: 108 + 144 = 252 144 + -24x + x2 = 252 Factor a perfect square on the left side: (x + -12)(x + -12) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + -12) equal to 15.874507866 and -15.874507866.Subproblem 1
x + -12 = 15.874507866 Simplifying x + -12 = 15.874507866 Reorder the terms: -12 + x = 15.874507866 Solving -12 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 15.874507866 + 12 Combine like terms: -12 + 12 = 0 0 + x = 15.874507866 + 12 x = 15.874507866 + 12 Combine like terms: 15.874507866 + 12 = 27.874507866 x = 27.874507866 Simplifying x = 27.874507866Subproblem 2
x + -12 = -15.874507866 Simplifying x + -12 = -15.874507866 Reorder the terms: -12 + x = -15.874507866 Solving -12 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -15.874507866 + 12 Combine like terms: -12 + 12 = 0 0 + x = -15.874507866 + 12 x = -15.874507866 + 12 Combine like terms: -15.874507866 + 12 = -3.874507866 x = -3.874507866 Simplifying x = -3.874507866Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.874507866, -3.874507866}
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