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Simplifying f2 + 22f = 20 Reorder the terms: 22f + f2 = 20 Solving 22f + f2 = 20 Solving for variable 'f'. Reorder the terms: -20 + 22f + f2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 22f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 22f + 20 + f2 = 0 + 20 Reorder the terms: -20 + 20 + 22f + f2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 22f + f2 = 0 + 20 22f + f2 = 0 + 20 Combine like terms: 0 + 20 = 20 22f + f2 = 20 The f term is 22f. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22f + 121 + f2 = 20 + 121 Reorder the terms: 121 + 22f + f2 = 20 + 121 Combine like terms: 20 + 121 = 141 121 + 22f + f2 = 141 Factor a perfect square on the left side: (f + 11)(f + 11) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (f + 11) equal to 11.874342087 and -11.874342087.Subproblem 1
f + 11 = 11.874342087 Simplifying f + 11 = 11.874342087 Reorder the terms: 11 + f = 11.874342087 Solving 11 + f = 11.874342087 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + f = 11.874342087 + -11 Combine like terms: 11 + -11 = 0 0 + f = 11.874342087 + -11 f = 11.874342087 + -11 Combine like terms: 11.874342087 + -11 = 0.874342087 f = 0.874342087 Simplifying f = 0.874342087Subproblem 2
f + 11 = -11.874342087 Simplifying f + 11 = -11.874342087 Reorder the terms: 11 + f = -11.874342087 Solving 11 + f = -11.874342087 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + f = -11.874342087 + -11 Combine like terms: 11 + -11 = 0 0 + f = -11.874342087 + -11 f = -11.874342087 + -11 Combine like terms: -11.874342087 + -11 = -22.874342087 f = -22.874342087 Simplifying f = -22.874342087Solution
The solution to the problem is based on the solutions from the subproblems. f = {0.874342087, -22.874342087}
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