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Simplifying x2 + 10x + -311 = 0 Reorder the terms: -311 + 10x + x2 = 0 Solving -311 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '311' to each side of the equation. -311 + 10x + 311 + x2 = 0 + 311 Reorder the terms: -311 + 311 + 10x + x2 = 0 + 311 Combine like terms: -311 + 311 = 0 0 + 10x + x2 = 0 + 311 10x + x2 = 0 + 311 Combine like terms: 0 + 311 = 311 10x + x2 = 311 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 311 + 25 Reorder the terms: 25 + 10x + x2 = 311 + 25 Combine like terms: 311 + 25 = 336 25 + 10x + x2 = 336 Factor a perfect square on the left side: (x + 5)(x + 5) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (x + 5) equal to 18.33030278 and -18.33030278.Subproblem 1
x + 5 = 18.33030278 Simplifying x + 5 = 18.33030278 Reorder the terms: 5 + x = 18.33030278 Solving 5 + x = 18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 18.33030278 + -5 Combine like terms: 5 + -5 = 0 0 + x = 18.33030278 + -5 x = 18.33030278 + -5 Combine like terms: 18.33030278 + -5 = 13.33030278 x = 13.33030278 Simplifying x = 13.33030278Subproblem 2
x + 5 = -18.33030278 Simplifying x + 5 = -18.33030278 Reorder the terms: 5 + x = -18.33030278 Solving 5 + x = -18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -18.33030278 + -5 Combine like terms: 5 + -5 = 0 0 + x = -18.33030278 + -5 x = -18.33030278 + -5 Combine like terms: -18.33030278 + -5 = -23.33030278 x = -23.33030278 Simplifying x = -23.33030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.33030278, -23.33030278}
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