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Simplifying x2 + 31x + 43 = 0 Reorder the terms: 43 + 31x + x2 = 0 Solving 43 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 31x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 31x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 31x + x2 = 0 + -43 31x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 31x + x2 = -43 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = -43 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -43 + 240.25 Combine like terms: -43 + 240.25 = 197.25 240.25 + 31x + x2 = 197.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 197.25 Calculate the square root of the right side: 14.044571905 Break this problem into two subproblems by setting (x + 15.5) equal to 14.044571905 and -14.044571905.Subproblem 1
x + 15.5 = 14.044571905 Simplifying x + 15.5 = 14.044571905 Reorder the terms: 15.5 + x = 14.044571905 Solving 15.5 + x = 14.044571905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 14.044571905 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 14.044571905 + -15.5 x = 14.044571905 + -15.5 Combine like terms: 14.044571905 + -15.5 = -1.455428095 x = -1.455428095 Simplifying x = -1.455428095Subproblem 2
x + 15.5 = -14.044571905 Simplifying x + 15.5 = -14.044571905 Reorder the terms: 15.5 + x = -14.044571905 Solving 15.5 + x = -14.044571905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -14.044571905 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -14.044571905 + -15.5 x = -14.044571905 + -15.5 Combine like terms: -14.044571905 + -15.5 = -29.544571905 x = -29.544571905 Simplifying x = -29.544571905Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.455428095, -29.544571905}
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