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Simplifying 0 = x2 + -11x + 22 Reorder the terms: 0 = 22 + -11x + x2 Solving 0 = 22 + -11x + x2 Solving for variable 'x'. Combine like terms: 0 + -22 = -22 -22 + 11x + -1x2 = 22 + -11x + x2 + -22 + 11x + -1x2 Reorder the terms: -22 + 11x + -1x2 = 22 + -22 + -11x + 11x + x2 + -1x2 Combine like terms: 22 + -22 = 0 -22 + 11x + -1x2 = 0 + -11x + 11x + x2 + -1x2 -22 + 11x + -1x2 = -11x + 11x + x2 + -1x2 Combine like terms: -11x + 11x = 0 -22 + 11x + -1x2 = 0 + x2 + -1x2 -22 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -22 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 22 + -11x + x2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -11x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -11x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -11x + x2 = 0 + -22 -11x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -11x + x2 = -22 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -22 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -22 + 30.25 Combine like terms: -22 + 30.25 = 8.25 30.25 + -11x + x2 = 8.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -5.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -5.5 = 2.872281323 Simplifying x + -5.5 = 2.872281323 Reorder the terms: -5.5 + x = 2.872281323 Solving -5.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.872281323 + 5.5 x = 2.872281323 + 5.5 Combine like terms: 2.872281323 + 5.5 = 8.372281323 x = 8.372281323 Simplifying x = 8.372281323Subproblem 2
x + -5.5 = -2.872281323 Simplifying x + -5.5 = -2.872281323 Reorder the terms: -5.5 + x = -2.872281323 Solving -5.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.872281323 + 5.5 x = -2.872281323 + 5.5 Combine like terms: -2.872281323 + 5.5 = 2.627718677 x = 2.627718677 Simplifying x = 2.627718677Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.372281323, 2.627718677}
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