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Simplifying x2 + 18x + -11664 = 0 Reorder the terms: -11664 + 18x + x2 = 0 Solving -11664 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11664' to each side of the equation. -11664 + 18x + 11664 + x2 = 0 + 11664 Reorder the terms: -11664 + 11664 + 18x + x2 = 0 + 11664 Combine like terms: -11664 + 11664 = 0 0 + 18x + x2 = 0 + 11664 18x + x2 = 0 + 11664 Combine like terms: 0 + 11664 = 11664 18x + x2 = 11664 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 = 11664 + 81 Reorder the terms: 81 + 18x + x2 = 11664 + 81 Combine like terms: 11664 + 81 = 11745 81 + 18x + x2 = 11745 Factor a perfect square on the left side: (x + 9)(x + 9) = 11745 Calculate the square root of the right side: 108.374351209 Break this problem into two subproblems by setting (x + 9) equal to 108.374351209 and -108.374351209.Subproblem 1
x + 9 = 108.374351209 Simplifying x + 9 = 108.374351209 Reorder the terms: 9 + x = 108.374351209 Solving 9 + x = 108.374351209 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 = 108.374351209 + -9 Combine like terms: 9 + -9 = 0 0 + x = 108.374351209 + -9 x = 108.374351209 + -9 Combine like terms: 108.374351209 + -9 = 99.374351209 x = 99.374351209 Simplifying x = 99.374351209Subproblem 2
x + 9 = -108.374351209 Simplifying x + 9 = -108.374351209 Reorder the terms: 9 + x = -108.374351209 Solving 9 + x = -108.374351209 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 = -108.374351209 + -9 Combine like terms: 9 + -9 = 0 0 + x = -108.374351209 + -9 x = -108.374351209 + -9 Combine like terms: -108.374351209 + -9 = -117.374351209 x = -117.374351209 Simplifying x = -117.374351209Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.374351209, -117.374351209}
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