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Simplifying x2 + -22x + 30 = 0 Reorder the terms: 30 + -22x + x2 = 0 Solving 30 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -22x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -22x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -22x + x2 = 0 + -30 -22x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -22x + x2 = -30 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 = -30 + 121 Reorder the terms: 121 + -22x + x2 = -30 + 121 Combine like terms: -30 + 121 = 91 121 + -22x + x2 = 91 Factor a perfect square on the left side: (x + -11)(x + -11) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -11) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -11 = 9.539392014 Simplifying x + -11 = 9.539392014 Reorder the terms: -11 + x = 9.539392014 Solving -11 + x = 9.539392014 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 = 9.539392014 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.539392014 + 11 x = 9.539392014 + 11 Combine like terms: 9.539392014 + 11 = 20.539392014 x = 20.539392014 Simplifying x = 20.539392014Subproblem 2
x + -11 = -9.539392014 Simplifying x + -11 = -9.539392014 Reorder the terms: -11 + x = -9.539392014 Solving -11 + x = -9.539392014 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 = -9.539392014 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.539392014 + 11 x = -9.539392014 + 11 Combine like terms: -9.539392014 + 11 = 1.460607986 x = 1.460607986 Simplifying x = 1.460607986Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.539392014, 1.460607986}
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