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Simplifying x2 + 30x + 31 = 0 Reorder the terms: 31 + 30x + x2 = 0 Solving 31 + 30x + 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 + 30x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 30x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 30x + x2 = 0 + -31 30x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 30x + x2 = -31 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -31 + 225 Reorder the terms: 225 + 30x + x2 = -31 + 225 Combine like terms: -31 + 225 = 194 225 + 30x + x2 = 194 Factor a perfect square on the left side: (x + 15)(x + 15) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (x + 15) equal to 13.928388277 and -13.928388277.Subproblem 1
x + 15 = 13.928388277 Simplifying x + 15 = 13.928388277 Reorder the terms: 15 + x = 13.928388277 Solving 15 + x = 13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 13.928388277 + -15 Combine like terms: 15 + -15 = 0 0 + x = 13.928388277 + -15 x = 13.928388277 + -15 Combine like terms: 13.928388277 + -15 = -1.071611723 x = -1.071611723 Simplifying x = -1.071611723Subproblem 2
x + 15 = -13.928388277 Simplifying x + 15 = -13.928388277 Reorder the terms: 15 + x = -13.928388277 Solving 15 + x = -13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -13.928388277 + -15 Combine like terms: 15 + -15 = 0 0 + x = -13.928388277 + -15 x = -13.928388277 + -15 Combine like terms: -13.928388277 + -15 = -28.928388277 x = -28.928388277 Simplifying x = -28.928388277Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.071611723, -28.928388277}
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