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Simplifying x2 + 18x + -41 = 0 Reorder the terms: -41 + 18x + x2 = 0 Solving -41 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 18x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 18x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 18x + x2 = 0 + 41 18x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 18x + x2 = 41 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 = 41 + 81 Reorder the terms: 81 + 18x + x2 = 41 + 81 Combine like terms: 41 + 81 = 122 81 + 18x + x2 = 122 Factor a perfect square on the left side: (x + 9)(x + 9) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (x + 9) equal to 11.045361017 and -11.045361017.Subproblem 1
x + 9 = 11.045361017 Simplifying x + 9 = 11.045361017 Reorder the terms: 9 + x = 11.045361017 Solving 9 + x = 11.045361017 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 = 11.045361017 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.045361017 + -9 x = 11.045361017 + -9 Combine like terms: 11.045361017 + -9 = 2.045361017 x = 2.045361017 Simplifying x = 2.045361017Subproblem 2
x + 9 = -11.045361017 Simplifying x + 9 = -11.045361017 Reorder the terms: 9 + x = -11.045361017 Solving 9 + x = -11.045361017 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 = -11.045361017 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.045361017 + -9 x = -11.045361017 + -9 Combine like terms: -11.045361017 + -9 = -20.045361017 x = -20.045361017 Simplifying x = -20.045361017Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.045361017, -20.045361017}
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