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Simplifying f2 + -4f = 29 Reorder the terms: -4f + f2 = 29 Solving -4f + f2 = 29 Solving for variable 'f'. Reorder the terms: -29 + -4f + f2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -4f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -4f + 29 + f2 = 0 + 29 Reorder the terms: -29 + 29 + -4f + f2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -4f + f2 = 0 + 29 -4f + f2 = 0 + 29 Combine like terms: 0 + 29 = 29 -4f + f2 = 29 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 = 29 + 4 Reorder the terms: 4 + -4f + f2 = 29 + 4 Combine like terms: 29 + 4 = 33 4 + -4f + f2 = 33 Factor a perfect square on the left side: (f + -2)(f + -2) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (f + -2) equal to 5.744562647 and -5.744562647.Subproblem 1
f + -2 = 5.744562647 Simplifying f + -2 = 5.744562647 Reorder the terms: -2 + f = 5.744562647 Solving -2 + f = 5.744562647 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 = 5.744562647 + 2 Combine like terms: -2 + 2 = 0 0 + f = 5.744562647 + 2 f = 5.744562647 + 2 Combine like terms: 5.744562647 + 2 = 7.744562647 f = 7.744562647 Simplifying f = 7.744562647Subproblem 2
f + -2 = -5.744562647 Simplifying f + -2 = -5.744562647 Reorder the terms: -2 + f = -5.744562647 Solving -2 + f = -5.744562647 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 = -5.744562647 + 2 Combine like terms: -2 + 2 = 0 0 + f = -5.744562647 + 2 f = -5.744562647 + 2 Combine like terms: -5.744562647 + 2 = -3.744562647 f = -3.744562647 Simplifying f = -3.744562647Solution
The solution to the problem is based on the solutions from the subproblems. f = {7.744562647, -3.744562647}
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