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Simplifying x2 + -22x + 48 = 0 Reorder the terms: 48 + -22x + x2 = 0 Solving 48 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -22x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -22x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -22x + x2 = 0 + -48 -22x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -22x + x2 = -48 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 = -48 + 121 Reorder the terms: 121 + -22x + x2 = -48 + 121 Combine like terms: -48 + 121 = 73 121 + -22x + x2 = 73 Factor a perfect square on the left side: (x + -11)(x + -11) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -11) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -11 = 8.544003745 Simplifying x + -11 = 8.544003745 Reorder the terms: -11 + x = 8.544003745 Solving -11 + x = 8.544003745 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 = 8.544003745 + 11 Combine like terms: -11 + 11 = 0 0 + x = 8.544003745 + 11 x = 8.544003745 + 11 Combine like terms: 8.544003745 + 11 = 19.544003745 x = 19.544003745 Simplifying x = 19.544003745Subproblem 2
x + -11 = -8.544003745 Simplifying x + -11 = -8.544003745 Reorder the terms: -11 + x = -8.544003745 Solving -11 + x = -8.544003745 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 = -8.544003745 + 11 Combine like terms: -11 + 11 = 0 0 + x = -8.544003745 + 11 x = -8.544003745 + 11 Combine like terms: -8.544003745 + 11 = 2.455996255 x = 2.455996255 Simplifying x = 2.455996255Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.544003745, 2.455996255}
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