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Simplifying x2 + 35x + 31 = 0 Reorder the terms: 31 + 35x + x2 = 0 Solving 31 + 35x + 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 + 35x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 35x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 35x + x2 = 0 + -31 35x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 35x + x2 = -31 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -31 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -31 + 306.25 Combine like terms: -31 + 306.25 = 275.25 306.25 + 35x + x2 = 275.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 275.25 Calculate the square root of the right side: 16.590660023 Break this problem into two subproblems by setting (x + 17.5) equal to 16.590660023 and -16.590660023.Subproblem 1
x + 17.5 = 16.590660023 Simplifying x + 17.5 = 16.590660023 Reorder the terms: 17.5 + x = 16.590660023 Solving 17.5 + x = 16.590660023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 16.590660023 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 16.590660023 + -17.5 x = 16.590660023 + -17.5 Combine like terms: 16.590660023 + -17.5 = -0.909339977 x = -0.909339977 Simplifying x = -0.909339977Subproblem 2
x + 17.5 = -16.590660023 Simplifying x + 17.5 = -16.590660023 Reorder the terms: 17.5 + x = -16.590660023 Solving 17.5 + x = -16.590660023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -16.590660023 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -16.590660023 + -17.5 x = -16.590660023 + -17.5 Combine like terms: -16.590660023 + -17.5 = -34.090660023 x = -34.090660023 Simplifying x = -34.090660023Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.909339977, -34.090660023}
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