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Simplifying x2 + 18x + 81 = 37 Reorder the terms: 81 + 18x + x2 = 37 Solving 81 + 18x + x2 = 37 Solving for variable 'x'. Reorder the terms: 81 + -37 + 18x + x2 = 37 + -37 Combine like terms: 81 + -37 = 44 44 + 18x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 44 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + 18x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + 18x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 18x + x2 = 0 + -44 18x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 18x + x2 = -44 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 = -44 + 81 Reorder the terms: 81 + 18x + x2 = -44 + 81 Combine like terms: -44 + 81 = 37 81 + 18x + x2 = 37 Factor a perfect square on the left side: (x + 9)(x + 9) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 9) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 9 = 6.08276253 Simplifying x + 9 = 6.08276253 Reorder the terms: 9 + x = 6.08276253 Solving 9 + x = 6.08276253 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 = 6.08276253 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.08276253 + -9 x = 6.08276253 + -9 Combine like terms: 6.08276253 + -9 = -2.91723747 x = -2.91723747 Simplifying x = -2.91723747Subproblem 2
x + 9 = -6.08276253 Simplifying x + 9 = -6.08276253 Reorder the terms: 9 + x = -6.08276253 Solving 9 + x = -6.08276253 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 = -6.08276253 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.08276253 + -9 x = -6.08276253 + -9 Combine like terms: -6.08276253 + -9 = -15.08276253 x = -15.08276253 Simplifying x = -15.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.91723747, -15.08276253}
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