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Simplifying x2 + 22x = -104 Reorder the terms: 22x + x2 = -104 Solving 22x + x2 = -104 Solving for variable 'x'. Reorder the terms: 104 + 22x + x2 = -104 + 104 Combine like terms: -104 + 104 = 0 104 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-104' to each side of the equation. 104 + 22x + -104 + x2 = 0 + -104 Reorder the terms: 104 + -104 + 22x + x2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + 22x + x2 = 0 + -104 22x + x2 = 0 + -104 Combine like terms: 0 + -104 = -104 22x + x2 = -104 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 = -104 + 121 Reorder the terms: 121 + 22x + x2 = -104 + 121 Combine like terms: -104 + 121 = 17 121 + 22x + x2 = 17 Factor a perfect square on the left side: (x + 11)(x + 11) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 11) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 11 = 4.123105626 Simplifying x + 11 = 4.123105626 Reorder the terms: 11 + x = 4.123105626 Solving 11 + x = 4.123105626 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 = 4.123105626 + -11 Combine like terms: 11 + -11 = 0 0 + x = 4.123105626 + -11 x = 4.123105626 + -11 Combine like terms: 4.123105626 + -11 = -6.876894374 x = -6.876894374 Simplifying x = -6.876894374Subproblem 2
x + 11 = -4.123105626 Simplifying x + 11 = -4.123105626 Reorder the terms: 11 + x = -4.123105626 Solving 11 + x = -4.123105626 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 = -4.123105626 + -11 Combine like terms: 11 + -11 = 0 0 + x = -4.123105626 + -11 x = -4.123105626 + -11 Combine like terms: -4.123105626 + -11 = -15.123105626 x = -15.123105626 Simplifying x = -15.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.876894374, -15.123105626}
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