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Simplifying f2 + -14f + 9 = 0 Reorder the terms: 9 + -14f + f2 = 0 Solving 9 + -14f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -14f + -9 + f2 = 0 + -9 Reorder the terms: 9 + -9 + -14f + f2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -14f + f2 = 0 + -9 -14f + f2 = 0 + -9 Combine like terms: 0 + -9 = -9 -14f + f2 = -9 The f term is -14f. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14f + 49 + f2 = -9 + 49 Reorder the terms: 49 + -14f + f2 = -9 + 49 Combine like terms: -9 + 49 = 40 49 + -14f + f2 = 40 Factor a perfect square on the left side: (f + -7)(f + -7) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (f + -7) equal to 6.32455532 and -6.32455532.Subproblem 1
f + -7 = 6.32455532 Simplifying f + -7 = 6.32455532 Reorder the terms: -7 + f = 6.32455532 Solving -7 + f = 6.32455532 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + f = 6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + f = 6.32455532 + 7 f = 6.32455532 + 7 Combine like terms: 6.32455532 + 7 = 13.32455532 f = 13.32455532 Simplifying f = 13.32455532Subproblem 2
f + -7 = -6.32455532 Simplifying f + -7 = -6.32455532 Reorder the terms: -7 + f = -6.32455532 Solving -7 + f = -6.32455532 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + f = -6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + f = -6.32455532 + 7 f = -6.32455532 + 7 Combine like terms: -6.32455532 + 7 = 0.67544468 f = 0.67544468 Simplifying f = 0.67544468Solution
The solution to the problem is based on the solutions from the subproblems. f = {13.32455532, 0.67544468}
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