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Simplifying x2 + 31x + 17 = 0 Reorder the terms: 17 + 31x + x2 = 0 Solving 17 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 31x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 31x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 31x + x2 = 0 + -17 31x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 31x + x2 = -17 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 = -17 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -17 + 240.25 Combine like terms: -17 + 240.25 = 223.25 240.25 + 31x + x2 = 223.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 223.25 Calculate the square root of the right side: 14.941552797 Break this problem into two subproblems by setting (x + 15.5) equal to 14.941552797 and -14.941552797.Subproblem 1
x + 15.5 = 14.941552797 Simplifying x + 15.5 = 14.941552797 Reorder the terms: 15.5 + x = 14.941552797 Solving 15.5 + x = 14.941552797 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 = 14.941552797 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 14.941552797 + -15.5 x = 14.941552797 + -15.5 Combine like terms: 14.941552797 + -15.5 = -0.558447203 x = -0.558447203 Simplifying x = -0.558447203Subproblem 2
x + 15.5 = -14.941552797 Simplifying x + 15.5 = -14.941552797 Reorder the terms: 15.5 + x = -14.941552797 Solving 15.5 + x = -14.941552797 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 = -14.941552797 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -14.941552797 + -15.5 x = -14.941552797 + -15.5 Combine like terms: -14.941552797 + -15.5 = -30.441552797 x = -30.441552797 Simplifying x = -30.441552797Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.558447203, -30.441552797}
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