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Simplifying 0 = x2 + -22x + -8 Reorder the terms: 0 = -8 + -22x + x2 Solving 0 = -8 + -22x + x2 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + 22x + -1x2 = -8 + -22x + x2 + 8 + 22x + -1x2 Reorder the terms: 8 + 22x + -1x2 = -8 + 8 + -22x + 22x + x2 + -1x2 Combine like terms: -8 + 8 = 0 8 + 22x + -1x2 = 0 + -22x + 22x + x2 + -1x2 8 + 22x + -1x2 = -22x + 22x + x2 + -1x2 Combine like terms: -22x + 22x = 0 8 + 22x + -1x2 = 0 + x2 + -1x2 8 + 22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + 22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -22x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -22x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -22x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -22x + x2 = 0 + 8 -22x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -22x + x2 = 8 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 8 + 121 Reorder the terms: 121 + -22x + x2 = 8 + 121 Combine like terms: 8 + 121 = 129 121 + -22x + x2 = 129 Factor a perfect square on the left side: (x + -11)(x + -11) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + -11) equal to 11.357816692 and -11.357816692.Subproblem 1
x + -11 = 11.357816692 Simplifying x + -11 = 11.357816692 Reorder the terms: -11 + x = 11.357816692 Solving -11 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 11.357816692 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.357816692 + 11 x = 11.357816692 + 11 Combine like terms: 11.357816692 + 11 = 22.357816692 x = 22.357816692 Simplifying x = 22.357816692Subproblem 2
x + -11 = -11.357816692 Simplifying x + -11 = -11.357816692 Reorder the terms: -11 + x = -11.357816692 Solving -11 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -11.357816692 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.357816692 + 11 x = -11.357816692 + 11 Combine like terms: -11.357816692 + 11 = -0.357816692 x = -0.357816692 Simplifying x = -0.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.357816692, -0.357816692}
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