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Simplifying x2 + 18x + 40 = 0 Reorder the terms: 40 + 18x + x2 = 0 Solving 40 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 18x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 18x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 18x + x2 = 0 + -40 18x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 18x + x2 = -40 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 = -40 + 81 Reorder the terms: 81 + 18x + x2 = -40 + 81 Combine like terms: -40 + 81 = 41 81 + 18x + x2 = 41 Factor a perfect square on the left side: (x + 9)(x + 9) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 9) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 9 = 6.403124237 Simplifying x + 9 = 6.403124237 Reorder the terms: 9 + x = 6.403124237 Solving 9 + x = 6.403124237 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 = 6.403124237 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.403124237 + -9 x = 6.403124237 + -9 Combine like terms: 6.403124237 + -9 = -2.596875763 x = -2.596875763 Simplifying x = -2.596875763Subproblem 2
x + 9 = -6.403124237 Simplifying x + 9 = -6.403124237 Reorder the terms: 9 + x = -6.403124237 Solving 9 + x = -6.403124237 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 = -6.403124237 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.403124237 + -9 x = -6.403124237 + -9 Combine like terms: -6.403124237 + -9 = -15.403124237 x = -15.403124237 Simplifying x = -15.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.596875763, -15.403124237}
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