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Simplifying x2 + 18x + 81 = 6 Reorder the terms: 81 + 18x + x2 = 6 Solving 81 + 18x + x2 = 6 Solving for variable 'x'. Reorder the terms: 81 + -6 + 18x + x2 = 6 + -6 Combine like terms: 81 + -6 = 75 75 + 18x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 75 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + 18x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + 18x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 18x + x2 = 0 + -75 18x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 18x + x2 = -75 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 = -75 + 81 Reorder the terms: 81 + 18x + x2 = -75 + 81 Combine like terms: -75 + 81 = 6 81 + 18x + x2 = 6 Factor a perfect square on the left side: (x + 9)(x + 9) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 9) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 9 = 2.449489743 Simplifying x + 9 = 2.449489743 Reorder the terms: 9 + x = 2.449489743 Solving 9 + x = 2.449489743 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 = 2.449489743 + -9 Combine like terms: 9 + -9 = 0 0 + x = 2.449489743 + -9 x = 2.449489743 + -9 Combine like terms: 2.449489743 + -9 = -6.550510257 x = -6.550510257 Simplifying x = -6.550510257Subproblem 2
x + 9 = -2.449489743 Simplifying x + 9 = -2.449489743 Reorder the terms: 9 + x = -2.449489743 Solving 9 + x = -2.449489743 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 = -2.449489743 + -9 Combine like terms: 9 + -9 = 0 0 + x = -2.449489743 + -9 x = -2.449489743 + -9 Combine like terms: -2.449489743 + -9 = -11.449489743 x = -11.449489743 Simplifying x = -11.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.550510257, -11.449489743}
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