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Simplifying 2x2 + -17x + 22 = 0 Reorder the terms: 22 + -17x + 2x2 = 0 Solving 22 + -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'. 11 + -8.5x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -8.5x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -8.5x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8.5x + x2 = 0 + -11 -8.5x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -8.5x + x2 = -11 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 = -11 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -11 + 18.0625 Combine like terms: -11 + 18.0625 = 7.0625 18.0625 + -8.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -4.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -4.25 = 2.657536453 Simplifying x + -4.25 = 2.657536453 Reorder the terms: -4.25 + x = 2.657536453 Solving -4.25 + x = 2.657536453 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 = 2.657536453 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 2.657536453 + 4.25 x = 2.657536453 + 4.25 Combine like terms: 2.657536453 + 4.25 = 6.907536453 x = 6.907536453 Simplifying x = 6.907536453Subproblem 2
x + -4.25 = -2.657536453 Simplifying x + -4.25 = -2.657536453 Reorder the terms: -4.25 + x = -2.657536453 Solving -4.25 + x = -2.657536453 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 = -2.657536453 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -2.657536453 + 4.25 x = -2.657536453 + 4.25 Combine like terms: -2.657536453 + 4.25 = 1.592463547 x = 1.592463547 Simplifying x = 1.592463547Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.907536453, 1.592463547}
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