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Simplifying 2400 + -160f + 2f2 = 1312.5 Solving 2400 + -160f + 2f2 = 1312.5 Solving for variable 'f'. Reorder the terms: 2400 + -1312.5 + -160f + 2f2 = 1312.5 + -1312.5 Combine like terms: 2400 + -1312.5 = 1087.5 1087.5 + -160f + 2f2 = 1312.5 + -1312.5 Combine like terms: 1312.5 + -1312.5 = 0.0 1087.5 + -160f + 2f2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 543.75 + -80f + f2 = 0.0 Move the constant term to the right: Add '-543.75' to each side of the equation. 543.75 + -80f + -543.75 + f2 = 0.0 + -543.75 Reorder the terms: 543.75 + -543.75 + -80f + f2 = 0.0 + -543.75 Combine like terms: 543.75 + -543.75 = 0.00 0.00 + -80f + f2 = 0.0 + -543.75 -80f + f2 = 0.0 + -543.75 Combine like terms: 0.0 + -543.75 = -543.75 -80f + f2 = -543.75 The f term is -80f. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80f + 1600 + f2 = -543.75 + 1600 Reorder the terms: 1600 + -80f + f2 = -543.75 + 1600 Combine like terms: -543.75 + 1600 = 1056.25 1600 + -80f + f2 = 1056.25 Factor a perfect square on the left side: (f + -40)(f + -40) = 1056.25 Calculate the square root of the right side: 32.5 Break this problem into two subproblems by setting (f + -40) equal to 32.5 and -32.5.Subproblem 1
f + -40 = 32.5 Simplifying f + -40 = 32.5 Reorder the terms: -40 + f = 32.5 Solving -40 + f = 32.5 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + f = 32.5 + 40 Combine like terms: -40 + 40 = 0 0 + f = 32.5 + 40 f = 32.5 + 40 Combine like terms: 32.5 + 40 = 72.5 f = 72.5 Simplifying f = 72.5Subproblem 2
f + -40 = -32.5 Simplifying f + -40 = -32.5 Reorder the terms: -40 + f = -32.5 Solving -40 + f = -32.5 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + f = -32.5 + 40 Combine like terms: -40 + 40 = 0 0 + f = -32.5 + 40 f = -32.5 + 40 Combine like terms: -32.5 + 40 = 7.5 f = 7.5 Simplifying f = 7.5Solution
The solution to the problem is based on the solutions from the subproblems. f = {72.5, 7.5}
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