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Simplifying 4f2 + 72f + -20 = 0 Reorder the terms: -20 + 72f + 4f2 = 0 Solving -20 + 72f + 4f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 18f + f2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 18f + f2)' equal to zero and attempt to solve: Simplifying -5 + 18f + f2 = 0 Solving -5 + 18f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 18f + 5 + f2 = 0 + 5 Reorder the terms: -5 + 5 + 18f + f2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 18f + f2 = 0 + 5 18f + f2 = 0 + 5 Combine like terms: 0 + 5 = 5 18f + f2 = 5 The f term is 18f. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18f + 81 + f2 = 5 + 81 Reorder the terms: 81 + 18f + f2 = 5 + 81 Combine like terms: 5 + 81 = 86 81 + 18f + f2 = 86 Factor a perfect square on the left side: (f + 9)(f + 9) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (f + 9) equal to 9.273618495 and -9.273618495.Subproblem 1
f + 9 = 9.273618495 Simplifying f + 9 = 9.273618495 Reorder the terms: 9 + f = 9.273618495 Solving 9 + f = 9.273618495 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + f = 9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + f = 9.273618495 + -9 f = 9.273618495 + -9 Combine like terms: 9.273618495 + -9 = 0.273618495 f = 0.273618495 Simplifying f = 0.273618495Subproblem 2
f + 9 = -9.273618495 Simplifying f + 9 = -9.273618495 Reorder the terms: 9 + f = -9.273618495 Solving 9 + f = -9.273618495 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + f = -9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + f = -9.273618495 + -9 f = -9.273618495 + -9 Combine like terms: -9.273618495 + -9 = -18.273618495 f = -18.273618495 Simplifying f = -18.273618495Solution
The solution to the problem is based on the solutions from the subproblems. f = {0.273618495, -18.273618495}Solution
f = {0.273618495, -18.273618495}
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