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Simplifying 3f2 + 39f + -63 = 0 Reorder the terms: -63 + 39f + 3f2 = 0 Solving -63 + 39f + 3f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + 13f + f2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-21 + 13f + f2)' equal to zero and attempt to solve: Simplifying -21 + 13f + f2 = 0 Solving -21 + 13f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 13f + 21 + f2 = 0 + 21 Reorder the terms: -21 + 21 + 13f + f2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 13f + f2 = 0 + 21 13f + f2 = 0 + 21 Combine like terms: 0 + 21 = 21 13f + f2 = 21 The f term is 13f. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13f + 42.25 + f2 = 21 + 42.25 Reorder the terms: 42.25 + 13f + f2 = 21 + 42.25 Combine like terms: 21 + 42.25 = 63.25 42.25 + 13f + f2 = 63.25 Factor a perfect square on the left side: (f + 6.5)(f + 6.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (f + 6.5) equal to 7.95298686 and -7.95298686.Subproblem 1
f + 6.5 = 7.95298686 Simplifying f + 6.5 = 7.95298686 Reorder the terms: 6.5 + f = 7.95298686 Solving 6.5 + f = 7.95298686 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + f = 7.95298686 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + f = 7.95298686 + -6.5 f = 7.95298686 + -6.5 Combine like terms: 7.95298686 + -6.5 = 1.45298686 f = 1.45298686 Simplifying f = 1.45298686Subproblem 2
f + 6.5 = -7.95298686 Simplifying f + 6.5 = -7.95298686 Reorder the terms: 6.5 + f = -7.95298686 Solving 6.5 + f = -7.95298686 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + f = -7.95298686 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + f = -7.95298686 + -6.5 f = -7.95298686 + -6.5 Combine like terms: -7.95298686 + -6.5 = -14.45298686 f = -14.45298686 Simplifying f = -14.45298686Solution
The solution to the problem is based on the solutions from the subproblems. f = {1.45298686, -14.45298686}Solution
f = {1.45298686, -14.45298686}
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