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Simplifying x2 + 31x + 46 = 0 Reorder the terms: 46 + 31x + x2 = 0 Solving 46 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + 31x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + 31x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 31x + x2 = 0 + -46 31x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 31x + x2 = -46 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 = -46 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -46 + 240.25 Combine like terms: -46 + 240.25 = 194.25 240.25 + 31x + x2 = 194.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 194.25 Calculate the square root of the right side: 13.937359865 Break this problem into two subproblems by setting (x + 15.5) equal to 13.937359865 and -13.937359865.Subproblem 1
x + 15.5 = 13.937359865 Simplifying x + 15.5 = 13.937359865 Reorder the terms: 15.5 + x = 13.937359865 Solving 15.5 + x = 13.937359865 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 = 13.937359865 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 13.937359865 + -15.5 x = 13.937359865 + -15.5 Combine like terms: 13.937359865 + -15.5 = -1.562640135 x = -1.562640135 Simplifying x = -1.562640135Subproblem 2
x + 15.5 = -13.937359865 Simplifying x + 15.5 = -13.937359865 Reorder the terms: 15.5 + x = -13.937359865 Solving 15.5 + x = -13.937359865 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 = -13.937359865 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -13.937359865 + -15.5 x = -13.937359865 + -15.5 Combine like terms: -13.937359865 + -15.5 = -29.437359865 x = -29.437359865 Simplifying x = -29.437359865Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.562640135, -29.437359865}
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