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Simplifying f2 + 4f + -39 = 0 Reorder the terms: -39 + 4f + f2 = 0 Solving -39 + 4f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 4f + 39 + f2 = 0 + 39 Reorder the terms: -39 + 39 + 4f + f2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 4f + f2 = 0 + 39 4f + f2 = 0 + 39 Combine like terms: 0 + 39 = 39 4f + f2 = 39 The f term is 4f. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4f + 4 + f2 = 39 + 4 Reorder the terms: 4 + 4f + f2 = 39 + 4 Combine like terms: 39 + 4 = 43 4 + 4f + f2 = 43 Factor a perfect square on the left side: (f + 2)(f + 2) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (f + 2) equal to 6.557438524 and -6.557438524.Subproblem 1
f + 2 = 6.557438524 Simplifying f + 2 = 6.557438524 Reorder the terms: 2 + f = 6.557438524 Solving 2 + f = 6.557438524 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + f = 6.557438524 + -2 Combine like terms: 2 + -2 = 0 0 + f = 6.557438524 + -2 f = 6.557438524 + -2 Combine like terms: 6.557438524 + -2 = 4.557438524 f = 4.557438524 Simplifying f = 4.557438524Subproblem 2
f + 2 = -6.557438524 Simplifying f + 2 = -6.557438524 Reorder the terms: 2 + f = -6.557438524 Solving 2 + f = -6.557438524 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + f = -6.557438524 + -2 Combine like terms: 2 + -2 = 0 0 + f = -6.557438524 + -2 f = -6.557438524 + -2 Combine like terms: -6.557438524 + -2 = -8.557438524 f = -8.557438524 Simplifying f = -8.557438524Solution
The solution to the problem is based on the solutions from the subproblems. f = {4.557438524, -8.557438524}
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