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Simplifying x2 + -22x + 2 = 8 Reorder the terms: 2 + -22x + x2 = 8 Solving 2 + -22x + x2 = 8 Solving for variable 'x'. Reorder the terms: 2 + -8 + -22x + x2 = 8 + -8 Combine like terms: 2 + -8 = -6 -6 + -22x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -6 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -22x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -22x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -22x + x2 = 0 + 6 -22x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -22x + x2 = 6 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 = 6 + 121 Reorder the terms: 121 + -22x + x2 = 6 + 121 Combine like terms: 6 + 121 = 127 121 + -22x + x2 = 127 Factor a perfect square on the left side: (x + -11)(x + -11) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (x + -11) equal to 11.26942767 and -11.26942767.Subproblem 1
x + -11 = 11.26942767 Simplifying x + -11 = 11.26942767 Reorder the terms: -11 + x = 11.26942767 Solving -11 + x = 11.26942767 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 = 11.26942767 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.26942767 + 11 x = 11.26942767 + 11 Combine like terms: 11.26942767 + 11 = 22.26942767 x = 22.26942767 Simplifying x = 22.26942767Subproblem 2
x + -11 = -11.26942767 Simplifying x + -11 = -11.26942767 Reorder the terms: -11 + x = -11.26942767 Solving -11 + x = -11.26942767 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 = -11.26942767 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.26942767 + 11 x = -11.26942767 + 11 Combine like terms: -11.26942767 + 11 = -0.26942767 x = -0.26942767 Simplifying x = -0.26942767Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.26942767, -0.26942767}
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