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Simplifying 2x2 + 17x + 34 = 0 Reorder the terms: 34 + 17x + 2x2 = 0 Solving 34 + 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'. 17 + 8.5x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + 8.5x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 8.5x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 8.5x + x2 = 0 + -17 8.5x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 8.5x + x2 = -17 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 = -17 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -17 + 18.0625 Combine like terms: -17 + 18.0625 = 1.0625 18.0625 + 8.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 4.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 4.25 = 1.030776406 Simplifying x + 4.25 = 1.030776406 Reorder the terms: 4.25 + x = 1.030776406 Solving 4.25 + x = 1.030776406 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 = 1.030776406 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 1.030776406 + -4.25 x = 1.030776406 + -4.25 Combine like terms: 1.030776406 + -4.25 = -3.219223594 x = -3.219223594 Simplifying x = -3.219223594Subproblem 2
x + 4.25 = -1.030776406 Simplifying x + 4.25 = -1.030776406 Reorder the terms: 4.25 + x = -1.030776406 Solving 4.25 + x = -1.030776406 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 = -1.030776406 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -1.030776406 + -4.25 x = -1.030776406 + -4.25 Combine like terms: -1.030776406 + -4.25 = -5.280776406 x = -5.280776406 Simplifying x = -5.280776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.219223594, -5.280776406}
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