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Simplifying x2 + 31x + 47 = 0 Reorder the terms: 47 + 31x + x2 = 0 Solving 47 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 31x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + 31x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 31x + x2 = 0 + -47 31x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 31x + x2 = -47 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 = -47 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -47 + 240.25 Combine like terms: -47 + 240.25 = 193.25 240.25 + 31x + x2 = 193.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 193.25 Calculate the square root of the right side: 13.901438774 Break this problem into two subproblems by setting (x + 15.5) equal to 13.901438774 and -13.901438774.Subproblem 1
x + 15.5 = 13.901438774 Simplifying x + 15.5 = 13.901438774 Reorder the terms: 15.5 + x = 13.901438774 Solving 15.5 + x = 13.901438774 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 = 13.901438774 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 13.901438774 + -15.5 x = 13.901438774 + -15.5 Combine like terms: 13.901438774 + -15.5 = -1.598561226 x = -1.598561226 Simplifying x = -1.598561226Subproblem 2
x + 15.5 = -13.901438774 Simplifying x + 15.5 = -13.901438774 Reorder the terms: 15.5 + x = -13.901438774 Solving 15.5 + x = -13.901438774 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 = -13.901438774 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -13.901438774 + -15.5 x = -13.901438774 + -15.5 Combine like terms: -13.901438774 + -15.5 = -29.401438774 x = -29.401438774 Simplifying x = -29.401438774Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.598561226, -29.401438774}
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