What are the solutions to the equation 75=-1/4 x^2+5x ?

The solutions to the equation 75=-1/4 x^2+5x are x=10-10sqrt(2)i,x=10+10sqrt(2)i

Find the zeros of 75=-1/4 x^2+5x

The zeros of 75=-1/4 x^2+5x are x=10-10sqrt(2)i,x=10+10sqrt(2)i

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75 = - \frac{1}{4} x^{2} + 5 x

x = 10 - 102 i, x = 10 + 102 i

Solution steps

75 = - \frac{1}{4} x^{2} + 5 x

Multiply both sides by

4

300 = - x^{2} + 20 x

Switch sides

- x^{2} + 20 x = 300

Move

300

to the left side

- x^{2} + 20 x - 300 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 20 \pm 2 0 ^{2} - 4 ( - 1 ) ( - 300 )}{2 ( - 1 )}

Simplify

2 0^{2} - 4 (- 1) (- 300) : 202 i

x_{1, 2} = \frac{- 20 \pm 20 2 i}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 20 + 20 2 i}{2 ( - 1 )}, x_{2} = \frac{- 20 - 20 2 i}{2 ( - 1 )}

x = \frac{- 20 + 20 2 i}{2 ( - 1 )} : 10 - 102 i

x = \frac{- 20 - 20 2 i}{2 ( - 1 )} : 10 + 102 i

The solutions to the quadratic equation are:

x = 10 - 102 i, x = 10 + 102 i

2 w^{2} - w - 21 = 0

n^{2} - 6 n + 7 = 0

(300 + 10 x) (1.6 - 0.01 x)

5 x^{2} - 8 x + 16 = 0

\frac{1}{5} k (k + 4) = 0.5

What are the solutions to the equation 75=-1/4 x^2+5x ?
The solutions to the equation 75=-1/4 x^2+5x are x=10-10sqrt(2)i,x=10+10sqrt(2)i
Find the zeros of 75=-1/4 x^2+5x
The zeros of 75=-1/4 x^2+5x are x=10-10sqrt(2)i,x=10+10sqrt(2)i