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Simplifying f2 + -28f = -13 Reorder the terms: -28f + f2 = -13 Solving -28f + f2 = -13 Solving for variable 'f'. Reorder the terms: 13 + -28f + f2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -28f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -28f + -13 + f2 = 0 + -13 Reorder the terms: 13 + -13 + -28f + f2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -28f + f2 = 0 + -13 -28f + f2 = 0 + -13 Combine like terms: 0 + -13 = -13 -28f + f2 = -13 The f term is -28f. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28f + 196 + f2 = -13 + 196 Reorder the terms: 196 + -28f + f2 = -13 + 196 Combine like terms: -13 + 196 = 183 196 + -28f + f2 = 183 Factor a perfect square on the left side: (f + -14)(f + -14) = 183 Calculate the square root of the right side: 13.527749258 Break this problem into two subproblems by setting (f + -14) equal to 13.527749258 and -13.527749258.Subproblem 1
f + -14 = 13.527749258 Simplifying f + -14 = 13.527749258 Reorder the terms: -14 + f = 13.527749258 Solving -14 + f = 13.527749258 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + f = 13.527749258 + 14 Combine like terms: -14 + 14 = 0 0 + f = 13.527749258 + 14 f = 13.527749258 + 14 Combine like terms: 13.527749258 + 14 = 27.527749258 f = 27.527749258 Simplifying f = 27.527749258Subproblem 2
f + -14 = -13.527749258 Simplifying f + -14 = -13.527749258 Reorder the terms: -14 + f = -13.527749258 Solving -14 + f = -13.527749258 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + f = -13.527749258 + 14 Combine like terms: -14 + 14 = 0 0 + f = -13.527749258 + 14 f = -13.527749258 + 14 Combine like terms: -13.527749258 + 14 = 0.472250742 f = 0.472250742 Simplifying f = 0.472250742Solution
The solution to the problem is based on the solutions from the subproblems. f = {27.527749258, 0.472250742}
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