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Simplifying x2 + 18x = -9 Reorder the terms: 18x + x2 = -9 Solving 18x + x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + 18x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 18x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 18x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 18x + x2 = 0 + -9 18x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 18x + x2 = -9 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 = -9 + 81 Reorder the terms: 81 + 18x + x2 = -9 + 81 Combine like terms: -9 + 81 = 72 81 + 18x + x2 = 72 Factor a perfect square on the left side: (x + 9)(x + 9) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + 9) equal to 8.485281374 and -8.485281374.Subproblem 1
x + 9 = 8.485281374 Simplifying x + 9 = 8.485281374 Reorder the terms: 9 + x = 8.485281374 Solving 9 + x = 8.485281374 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 = 8.485281374 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.485281374 + -9 x = 8.485281374 + -9 Combine like terms: 8.485281374 + -9 = -0.514718626 x = -0.514718626 Simplifying x = -0.514718626Subproblem 2
x + 9 = -8.485281374 Simplifying x + 9 = -8.485281374 Reorder the terms: 9 + x = -8.485281374 Solving 9 + x = -8.485281374 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 = -8.485281374 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.485281374 + -9 x = -8.485281374 + -9 Combine like terms: -8.485281374 + -9 = -17.485281374 x = -17.485281374 Simplifying x = -17.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.514718626, -17.485281374}
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