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Simplifying 2x2 + 17x = 115 Reorder the terms: 17x + 2x2 = 115 Solving 17x + 2x2 = 115 Solving for variable 'x'. Reorder the terms: -115 + 17x + 2x2 = 115 + -115 Combine like terms: 115 + -115 = 0 -115 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -57.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '57.5' to each side of the equation. -57.5 + 8.5x + 57.5 + x2 = 0 + 57.5 Reorder the terms: -57.5 + 57.5 + 8.5x + x2 = 0 + 57.5 Combine like terms: -57.5 + 57.5 = 0.0 0.0 + 8.5x + x2 = 0 + 57.5 8.5x + x2 = 0 + 57.5 Combine like terms: 0 + 57.5 = 57.5 8.5x + x2 = 57.5 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 = 57.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 57.5 + 18.0625 Combine like terms: 57.5 + 18.0625 = 75.5625 18.0625 + 8.5x + x2 = 75.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 75.5625 Calculate the square root of the right side: 8.692669325 Break this problem into two subproblems by setting (x + 4.25) equal to 8.692669325 and -8.692669325.Subproblem 1
x + 4.25 = 8.692669325 Simplifying x + 4.25 = 8.692669325 Reorder the terms: 4.25 + x = 8.692669325 Solving 4.25 + x = 8.692669325 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 = 8.692669325 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 8.692669325 + -4.25 x = 8.692669325 + -4.25 Combine like terms: 8.692669325 + -4.25 = 4.442669325 x = 4.442669325 Simplifying x = 4.442669325Subproblem 2
x + 4.25 = -8.692669325 Simplifying x + 4.25 = -8.692669325 Reorder the terms: 4.25 + x = -8.692669325 Solving 4.25 + x = -8.692669325 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 = -8.692669325 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -8.692669325 + -4.25 x = -8.692669325 + -4.25 Combine like terms: -8.692669325 + -4.25 = -12.942669325 x = -12.942669325 Simplifying x = -12.942669325Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.442669325, -12.942669325}
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