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Simplifying 2x2 + -17x + 31 = 0 Reorder the terms: 31 + -17x + 2x2 = 0 Solving 31 + -17x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + -8.5x + -15.5 + x2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + -8.5x + x2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + -8.5x + x2 = 0 + -15.5 -8.5x + x2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 -8.5x + x2 = -15.5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -15.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -15.5 + 18.0625 Combine like terms: -15.5 + 18.0625 = 2.5625 18.0625 + -8.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -4.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -4.25 = 1.600781059 Simplifying x + -4.25 = 1.600781059 Reorder the terms: -4.25 + x = 1.600781059 Solving -4.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 1.600781059 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 1.600781059 + 4.25 x = 1.600781059 + 4.25 Combine like terms: 1.600781059 + 4.25 = 5.850781059 x = 5.850781059 Simplifying x = 5.850781059Subproblem 2
x + -4.25 = -1.600781059 Simplifying x + -4.25 = -1.600781059 Reorder the terms: -4.25 + x = -1.600781059 Solving -4.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -1.600781059 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -1.600781059 + 4.25 x = -1.600781059 + 4.25 Combine like terms: -1.600781059 + 4.25 = 2.649218941 x = 2.649218941 Simplifying x = 2.649218941Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.850781059, 2.649218941}
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