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Simplifying x2 + -17x + 22 = 0 Reorder the terms: 22 + -17x + x2 = 0 Solving 22 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -17x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -17x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -17x + x2 = 0 + -22 -17x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -17x + x2 = -22 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -22 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -22 + 72.25 Combine like terms: -22 + 72.25 = 50.25 72.25 + -17x + x2 = 50.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -8.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -8.5 = 7.088723439 Simplifying x + -8.5 = 7.088723439 Reorder the terms: -8.5 + x = 7.088723439 Solving -8.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 7.088723439 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.088723439 + 8.5 x = 7.088723439 + 8.5 Combine like terms: 7.088723439 + 8.5 = 15.588723439 x = 15.588723439 Simplifying x = 15.588723439Subproblem 2
x + -8.5 = -7.088723439 Simplifying x + -8.5 = -7.088723439 Reorder the terms: -8.5 + x = -7.088723439 Solving -8.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -7.088723439 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.088723439 + 8.5 x = -7.088723439 + 8.5 Combine like terms: -7.088723439 + 8.5 = 1.411276561 x = 1.411276561 Simplifying x = 1.411276561Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.588723439, 1.411276561}
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