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Simplifying f2 + -7f + -4 = 0 Reorder the terms: -4 + -7f + f2 = 0 Solving -4 + -7f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -7f + 4 + f2 = 0 + 4 Reorder the terms: -4 + 4 + -7f + f2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7f + f2 = 0 + 4 -7f + f2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7f + f2 = 4 The f term is -7f. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7f + 12.25 + f2 = 4 + 12.25 Reorder the terms: 12.25 + -7f + f2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + -7f + f2 = 16.25 Factor a perfect square on the left side: (f + -3.5)(f + -3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (f + -3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
f + -3.5 = 4.031128874 Simplifying f + -3.5 = 4.031128874 Reorder the terms: -3.5 + f = 4.031128874 Solving -3.5 + f = 4.031128874 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + f = 4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + f = 4.031128874 + 3.5 f = 4.031128874 + 3.5 Combine like terms: 4.031128874 + 3.5 = 7.531128874 f = 7.531128874 Simplifying f = 7.531128874Subproblem 2
f + -3.5 = -4.031128874 Simplifying f + -3.5 = -4.031128874 Reorder the terms: -3.5 + f = -4.031128874 Solving -3.5 + f = -4.031128874 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + f = -4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + f = -4.031128874 + 3.5 f = -4.031128874 + 3.5 Combine like terms: -4.031128874 + 3.5 = -0.531128874 f = -0.531128874 Simplifying f = -0.531128874Solution
The solution to the problem is based on the solutions from the subproblems. f = {7.531128874, -0.531128874}
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