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Simplifying x2 + 22x = -13 Reorder the terms: 22x + x2 = -13 Solving 22x + x2 = -13 Solving for variable 'x'. Reorder the terms: 13 + 22x + x2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 22x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 22x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 22x + x2 = 0 + -13 22x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 22x + x2 = -13 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 = -13 + 121 Reorder the terms: 121 + 22x + x2 = -13 + 121 Combine like terms: -13 + 121 = 108 121 + 22x + x2 = 108 Factor a perfect square on the left side: (x + 11)(x + 11) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + 11) equal to 10.392304845 and -10.392304845.Subproblem 1
x + 11 = 10.392304845 Simplifying x + 11 = 10.392304845 Reorder the terms: 11 + x = 10.392304845 Solving 11 + x = 10.392304845 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 = 10.392304845 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.392304845 + -11 x = 10.392304845 + -11 Combine like terms: 10.392304845 + -11 = -0.607695155 x = -0.607695155 Simplifying x = -0.607695155Subproblem 2
x + 11 = -10.392304845 Simplifying x + 11 = -10.392304845 Reorder the terms: 11 + x = -10.392304845 Solving 11 + x = -10.392304845 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 = -10.392304845 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.392304845 + -11 x = -10.392304845 + -11 Combine like terms: -10.392304845 + -11 = -21.392304845 x = -21.392304845 Simplifying x = -21.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.607695155, -21.392304845}
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