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Simplifying x2 + 18x + -240 = 0 Reorder the terms: -240 + 18x + x2 = 0 Solving -240 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 18x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 18x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 18x + x2 = 0 + 240 18x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 18x + x2 = 240 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 = 240 + 81 Reorder the terms: 81 + 18x + x2 = 240 + 81 Combine like terms: 240 + 81 = 321 81 + 18x + x2 = 321 Factor a perfect square on the left side: (x + 9)(x + 9) = 321 Calculate the square root of the right side: 17.916472867 Break this problem into two subproblems by setting (x + 9) equal to 17.916472867 and -17.916472867.Subproblem 1
x + 9 = 17.916472867 Simplifying x + 9 = 17.916472867 Reorder the terms: 9 + x = 17.916472867 Solving 9 + x = 17.916472867 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 = 17.916472867 + -9 Combine like terms: 9 + -9 = 0 0 + x = 17.916472867 + -9 x = 17.916472867 + -9 Combine like terms: 17.916472867 + -9 = 8.916472867 x = 8.916472867 Simplifying x = 8.916472867Subproblem 2
x + 9 = -17.916472867 Simplifying x + 9 = -17.916472867 Reorder the terms: 9 + x = -17.916472867 Solving 9 + x = -17.916472867 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 = -17.916472867 + -9 Combine like terms: 9 + -9 = 0 0 + x = -17.916472867 + -9 x = -17.916472867 + -9 Combine like terms: -17.916472867 + -9 = -26.916472867 x = -26.916472867 Simplifying x = -26.916472867Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.916472867, -26.916472867}
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