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Simplifying f2 + -10f = 33 Reorder the terms: -10f + f2 = 33 Solving -10f + f2 = 33 Solving for variable 'f'. Reorder the terms: -33 + -10f + f2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -10f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -10f + 33 + f2 = 0 + 33 Reorder the terms: -33 + 33 + -10f + f2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -10f + f2 = 0 + 33 -10f + f2 = 0 + 33 Combine like terms: 0 + 33 = 33 -10f + f2 = 33 The f term is -10f. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10f + 25 + f2 = 33 + 25 Reorder the terms: 25 + -10f + f2 = 33 + 25 Combine like terms: 33 + 25 = 58 25 + -10f + f2 = 58 Factor a perfect square on the left side: (f + -5)(f + -5) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (f + -5) equal to 7.615773106 and -7.615773106.Subproblem 1
f + -5 = 7.615773106 Simplifying f + -5 = 7.615773106 Reorder the terms: -5 + f = 7.615773106 Solving -5 + f = 7.615773106 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + f = 7.615773106 + 5 Combine like terms: -5 + 5 = 0 0 + f = 7.615773106 + 5 f = 7.615773106 + 5 Combine like terms: 7.615773106 + 5 = 12.615773106 f = 12.615773106 Simplifying f = 12.615773106Subproblem 2
f + -5 = -7.615773106 Simplifying f + -5 = -7.615773106 Reorder the terms: -5 + f = -7.615773106 Solving -5 + f = -7.615773106 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + f = -7.615773106 + 5 Combine like terms: -5 + 5 = 0 0 + f = -7.615773106 + 5 f = -7.615773106 + 5 Combine like terms: -7.615773106 + 5 = -2.615773106 f = -2.615773106 Simplifying f = -2.615773106Solution
The solution to the problem is based on the solutions from the subproblems. f = {12.615773106, -2.615773106}
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