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Simplifying x2 + 22x + -6 = 0 Reorder the terms: -6 + 22x + x2 = 0 Solving -6 + 22x + x2 = 0 Solving for variable 'x'. 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 = 0.26942767 x = 0.26942767 Simplifying x = 0.26942767Subproblem 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 = -22.26942767 x = -22.26942767 Simplifying x = -22.26942767Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.26942767, -22.26942767}
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