What are the solutions to the equation 7f+f^2=60 ?

The solutions to the equation 7f+f^2=60 are f=5,f=-12

Find the zeros of 7f+f^2=60

The zeros of 7f+f^2=60 are f=5,f=-12

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7 f + f^{2} = 60

f = 5, f = - 12

Solution steps

7 f + f^{2} = 60

Move

60

to the left side

7 f + f^{2} - 60 = 0

Write in the standard form

a x^{2} + b x + c = 0

f^{2} + 7 f - 60 = 0

Solve with the quadratic formula

f_{1, 2} = \frac{- 7 \pm 7 ^{2} - 4 \cdot 1 \cdot ( - 60 )}{2 \cdot 1}

7^{2} - 4 \cdot 1 \cdot (- 60) = 17

f_{1, 2} = \frac{- 7 \pm 17}{2 \cdot 1}

Separate the solutions

f_{1} = \frac{- 7 + 17}{2 \cdot 1}, f_{2} = \frac{- 7 - 17}{2 \cdot 1}

f = \frac{- 7 + 17}{2 \cdot 1} : 5

f = \frac{- 7 - 17}{2 \cdot 1} : - 12

The solutions to the quadratic equation are:

f = 5, f = - 12

5^{2} - 2^{2} = x^{2}

z^{2} - 3^{\frac{1}{2}} z - 6 = 0

x, x^{2} - 3 x y + y^{1} = 1

x^{2} + 4 - 8 = 0

5 x^{2} - 9 x - 2 = 2 x

What are the solutions to the equation 7f+f^2=60 ?
The solutions to the equation 7f+f^2=60 are f=5,f=-12
Find the zeros of 7f+f^2=60
The zeros of 7f+f^2=60 are f=5,f=-12