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Simplifying x2 + 22x = -6 Reorder the terms: 22x + x2 = -6 Solving 22x + x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 22x + x2 = -6 + 6 Combine like terms: -6 + 6 = 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 = 115 121 + 22x + x2 = 115 Factor a perfect square on the left side: (x + 11)(x + 11) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + 11) equal to 10.723805295 and -10.723805295.Subproblem 1
x + 11 = 10.723805295 Simplifying x + 11 = 10.723805295 Reorder the terms: 11 + x = 10.723805295 Solving 11 + x = 10.723805295 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 = 10.723805295 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.723805295 + -11 x = 10.723805295 + -11 Combine like terms: 10.723805295 + -11 = -0.276194705 x = -0.276194705 Simplifying x = -0.276194705Subproblem 2
x + 11 = -10.723805295 Simplifying x + 11 = -10.723805295 Reorder the terms: 11 + x = -10.723805295 Solving 11 + x = -10.723805295 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 = -10.723805295 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.723805295 + -11 x = -10.723805295 + -11 Combine like terms: -10.723805295 + -11 = -21.723805295 x = -21.723805295 Simplifying x = -21.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.276194705, -21.723805295}
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