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Simplifying x2 + 18x + 22 = -8 Reorder the terms: 22 + 18x + x2 = -8 Solving 22 + 18x + x2 = -8 Solving for variable 'x'. Reorder the terms: 22 + 8 + 18x + x2 = -8 + 8 Combine like terms: 22 + 8 = 30 30 + 18x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 30 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 18x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 18x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 18x + x2 = 0 + -30 18x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 18x + x2 = -30 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 = -30 + 81 Reorder the terms: 81 + 18x + x2 = -30 + 81 Combine like terms: -30 + 81 = 51 81 + 18x + x2 = 51 Factor a perfect square on the left side: (x + 9)(x + 9) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + 9) equal to 7.141428429 and -7.141428429.Subproblem 1
x + 9 = 7.141428429 Simplifying x + 9 = 7.141428429 Reorder the terms: 9 + x = 7.141428429 Solving 9 + x = 7.141428429 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 = 7.141428429 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.141428429 + -9 x = 7.141428429 + -9 Combine like terms: 7.141428429 + -9 = -1.858571571 x = -1.858571571 Simplifying x = -1.858571571Subproblem 2
x + 9 = -7.141428429 Simplifying x + 9 = -7.141428429 Reorder the terms: 9 + x = -7.141428429 Solving 9 + x = -7.141428429 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 = -7.141428429 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.141428429 + -9 x = -7.141428429 + -9 Combine like terms: -7.141428429 + -9 = -16.141428429 x = -16.141428429 Simplifying x = -16.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.858571571, -16.141428429}
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