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Simplifying x2 + 18x + 27 = -7 Reorder the terms: 27 + 18x + x2 = -7 Solving 27 + 18x + x2 = -7 Solving for variable 'x'. Reorder the terms: 27 + 7 + 18x + x2 = -7 + 7 Combine like terms: 27 + 7 = 34 34 + 18x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 34 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 18x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 18x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 18x + x2 = 0 + -34 18x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 18x + x2 = -34 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 = -34 + 81 Reorder the terms: 81 + 18x + x2 = -34 + 81 Combine like terms: -34 + 81 = 47 81 + 18x + x2 = 47 Factor a perfect square on the left side: (x + 9)(x + 9) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + 9) equal to 6.8556546 and -6.8556546.Subproblem 1
x + 9 = 6.8556546 Simplifying x + 9 = 6.8556546 Reorder the terms: 9 + x = 6.8556546 Solving 9 + x = 6.8556546 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 = 6.8556546 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.8556546 + -9 x = 6.8556546 + -9 Combine like terms: 6.8556546 + -9 = -2.1443454 x = -2.1443454 Simplifying x = -2.1443454Subproblem 2
x + 9 = -6.8556546 Simplifying x + 9 = -6.8556546 Reorder the terms: 9 + x = -6.8556546 Solving 9 + x = -6.8556546 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 = -6.8556546 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.8556546 + -9 x = -6.8556546 + -9 Combine like terms: -6.8556546 + -9 = -15.8556546 x = -15.8556546 Simplifying x = -15.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.1443454, -15.8556546}
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