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Simplifying f2 + -24f = 1 Reorder the terms: -24f + f2 = 1 Solving -24f + f2 = 1 Solving for variable 'f'. Reorder the terms: -1 + -24f + f2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -24f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -24f + 1 + f2 = 0 + 1 Reorder the terms: -1 + 1 + -24f + f2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -24f + f2 = 0 + 1 -24f + f2 = 0 + 1 Combine like terms: 0 + 1 = 1 -24f + f2 = 1 The f term is -24f. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24f + 144 + f2 = 1 + 144 Reorder the terms: 144 + -24f + f2 = 1 + 144 Combine like terms: 1 + 144 = 145 144 + -24f + f2 = 145 Factor a perfect square on the left side: (f + -12)(f + -12) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (f + -12) equal to 12.041594579 and -12.041594579.Subproblem 1
f + -12 = 12.041594579 Simplifying f + -12 = 12.041594579 Reorder the terms: -12 + f = 12.041594579 Solving -12 + f = 12.041594579 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + f = 12.041594579 + 12 Combine like terms: -12 + 12 = 0 0 + f = 12.041594579 + 12 f = 12.041594579 + 12 Combine like terms: 12.041594579 + 12 = 24.041594579 f = 24.041594579 Simplifying f = 24.041594579Subproblem 2
f + -12 = -12.041594579 Simplifying f + -12 = -12.041594579 Reorder the terms: -12 + f = -12.041594579 Solving -12 + f = -12.041594579 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + f = -12.041594579 + 12 Combine like terms: -12 + 12 = 0 0 + f = -12.041594579 + 12 f = -12.041594579 + 12 Combine like terms: -12.041594579 + 12 = -0.041594579 f = -0.041594579 Simplifying f = -0.041594579Solution
The solution to the problem is based on the solutions from the subproblems. f = {24.041594579, -0.041594579}
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