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Simplifying x2 + 20x + 31 = 0 Reorder the terms: 31 + 20x + x2 = 0 Solving 31 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 20x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 20x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 20x + x2 = 0 + -31 20x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 20x + x2 = -31 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -31 + 100 Reorder the terms: 100 + 20x + x2 = -31 + 100 Combine like terms: -31 + 100 = 69 100 + 20x + x2 = 69 Factor a perfect square on the left side: (x + 10)(x + 10) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + 10) equal to 8.306623863 and -8.306623863.Subproblem 1
x + 10 = 8.306623863 Simplifying x + 10 = 8.306623863 Reorder the terms: 10 + x = 8.306623863 Solving 10 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 8.306623863 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.306623863 + -10 x = 8.306623863 + -10 Combine like terms: 8.306623863 + -10 = -1.693376137 x = -1.693376137 Simplifying x = -1.693376137Subproblem 2
x + 10 = -8.306623863 Simplifying x + 10 = -8.306623863 Reorder the terms: 10 + x = -8.306623863 Solving 10 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -8.306623863 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.306623863 + -10 x = -8.306623863 + -10 Combine like terms: -8.306623863 + -10 = -18.306623863 x = -18.306623863 Simplifying x = -18.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.693376137, -18.306623863}
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