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Simplifying x2 + 18x = -13 Reorder the terms: 18x + x2 = -13 Solving 18x + x2 = -13 Solving for variable 'x'. Reorder the terms: 13 + 18x + x2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 18x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 18x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 18x + x2 = 0 + -13 18x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 18x + x2 = -13 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 = -13 + 81 Reorder the terms: 81 + 18x + x2 = -13 + 81 Combine like terms: -13 + 81 = 68 81 + 18x + x2 = 68 Factor a perfect square on the left side: (x + 9)(x + 9) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + 9) equal to 8.246211251 and -8.246211251.Subproblem 1
x + 9 = 8.246211251 Simplifying x + 9 = 8.246211251 Reorder the terms: 9 + x = 8.246211251 Solving 9 + x = 8.246211251 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 = 8.246211251 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.246211251 + -9 x = 8.246211251 + -9 Combine like terms: 8.246211251 + -9 = -0.753788749 x = -0.753788749 Simplifying x = -0.753788749Subproblem 2
x + 9 = -8.246211251 Simplifying x + 9 = -8.246211251 Reorder the terms: 9 + x = -8.246211251 Solving 9 + x = -8.246211251 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 = -8.246211251 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.246211251 + -9 x = -8.246211251 + -9 Combine like terms: -8.246211251 + -9 = -17.246211251 x = -17.246211251 Simplifying x = -17.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.753788749, -17.246211251}
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