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Simplifying x2 + 18x + -224 = 0 Reorder the terms: -224 + 18x + x2 = 0 Solving -224 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + 18x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 18x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 18x + x2 = 0 + 224 18x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 18x + x2 = 224 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 = 224 + 81 Reorder the terms: 81 + 18x + x2 = 224 + 81 Combine like terms: 224 + 81 = 305 81 + 18x + x2 = 305 Factor a perfect square on the left side: (x + 9)(x + 9) = 305 Calculate the square root of the right side: 17.464249197 Break this problem into two subproblems by setting (x + 9) equal to 17.464249197 and -17.464249197.Subproblem 1
x + 9 = 17.464249197 Simplifying x + 9 = 17.464249197 Reorder the terms: 9 + x = 17.464249197 Solving 9 + x = 17.464249197 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 = 17.464249197 + -9 Combine like terms: 9 + -9 = 0 0 + x = 17.464249197 + -9 x = 17.464249197 + -9 Combine like terms: 17.464249197 + -9 = 8.464249197 x = 8.464249197 Simplifying x = 8.464249197Subproblem 2
x + 9 = -17.464249197 Simplifying x + 9 = -17.464249197 Reorder the terms: 9 + x = -17.464249197 Solving 9 + x = -17.464249197 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 = -17.464249197 + -9 Combine like terms: 9 + -9 = 0 0 + x = -17.464249197 + -9 x = -17.464249197 + -9 Combine like terms: -17.464249197 + -9 = -26.464249197 x = -26.464249197 Simplifying x = -26.464249197Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.464249197, -26.464249197}
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