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Simplifying x2 + 18x + 42 = 0 Reorder the terms: 42 + 18x + x2 = 0 Solving 42 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 18x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + 18x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 18x + x2 = 0 + -42 18x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 18x + x2 = -42 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 = -42 + 81 Reorder the terms: 81 + 18x + x2 = -42 + 81 Combine like terms: -42 + 81 = 39 81 + 18x + x2 = 39 Factor a perfect square on the left side: (x + 9)(x + 9) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 9) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 9 = 6.244997998 Simplifying x + 9 = 6.244997998 Reorder the terms: 9 + x = 6.244997998 Solving 9 + x = 6.244997998 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 = 6.244997998 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.244997998 + -9 x = 6.244997998 + -9 Combine like terms: 6.244997998 + -9 = -2.755002002 x = -2.755002002 Simplifying x = -2.755002002Subproblem 2
x + 9 = -6.244997998 Simplifying x + 9 = -6.244997998 Reorder the terms: 9 + x = -6.244997998 Solving 9 + x = -6.244997998 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 = -6.244997998 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.244997998 + -9 x = -6.244997998 + -9 Combine like terms: -6.244997998 + -9 = -15.244997998 x = -15.244997998 Simplifying x = -15.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.755002002, -15.244997998}
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