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Simplifying x2 + 18x + -123 = 0 Reorder the terms: -123 + 18x + x2 = 0 Solving -123 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '123' to each side of the equation. -123 + 18x + 123 + x2 = 0 + 123 Reorder the terms: -123 + 123 + 18x + x2 = 0 + 123 Combine like terms: -123 + 123 = 0 0 + 18x + x2 = 0 + 123 18x + x2 = 0 + 123 Combine like terms: 0 + 123 = 123 18x + x2 = 123 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 123 + 81 Reorder the terms: 81 + 18x + x2 = 123 + 81 Combine like terms: 123 + 81 = 204 81 + 18x + x2 = 204 Factor a perfect square on the left side: (x + 9)(x + 9) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + 9) equal to 14.282856857 and -14.282856857.Subproblem 1
x + 9 = 14.282856857 Simplifying x + 9 = 14.282856857 Reorder the terms: 9 + x = 14.282856857 Solving 9 + x = 14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 14.282856857 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.282856857 + -9 x = 14.282856857 + -9 Combine like terms: 14.282856857 + -9 = 5.282856857 x = 5.282856857 Simplifying x = 5.282856857Subproblem 2
x + 9 = -14.282856857 Simplifying x + 9 = -14.282856857 Reorder the terms: 9 + x = -14.282856857 Solving 9 + x = -14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -14.282856857 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.282856857 + -9 x = -14.282856857 + -9 Combine like terms: -14.282856857 + -9 = -23.282856857 x = -23.282856857 Simplifying x = -23.282856857Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.282856857, -23.282856857}
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