What are the solutions to the equation (x)=-4x+0.05x^2+240 ?

The solutions to the equation (x)=-4x+0.05x^2+240 are x=50+10sqrt(23)i,x=50-10sqrt(23)i

Find the zeros of (x)=-4x+0.05x^2+240

The zeros of (x)=-4x+0.05x^2+240 are x=50+10sqrt(23)i,x=50-10sqrt(23)i

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(x) = - 4 x + 0.05 x^{2} + 240

x = 50 + 1023 i, x = 50 - 1023 i

Solution steps

(x) = - 4 x + 0.05 x^{2} + 240

Multiply both sides by

100

x \cdot 100 = - 400 x + 5 x^{2} + 24000

Switch sides

- 400 x + 5 x^{2} + 24000 = x \cdot 100

Move

x 100

to the left side

5 x^{2} - 500 x + 24000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 500 ) \pm ( - 500 ) ^{2} - 4 \cdot 5 \cdot 24000}{2 \cdot 5}

Simplify

(- 500)^{2} - 4 \cdot 5 \cdot 24000 : 10023 i

x_{1, 2} = \frac{- ( - 500 ) \pm 100 23 i}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 500 ) + 100 23 i}{2 \cdot 5}, x_{2} = \frac{- ( - 500 ) - 100 23 i}{2 \cdot 5}

x = \frac{- ( - 500 ) + 100 23 i}{2 \cdot 5} : 50 + 1023 i

x = \frac{- ( - 500 ) - 100 23 i}{2 \cdot 5} : 50 - 1023 i

The solutions to the quadratic equation are:

x = 50 + 1023 i, x = 50 - 1023 i

(7 x + 5)^{2} + 7 (7 x + 5) = 0

x^{2} - 3 x - 6 = 2 x + 30

x, x^{2} + 4 x - 8 = 0

x^{2} - 8 x + 3 = 0

X^{2} + 3 X + 1 = 0

What are the solutions to the equation (x)=-4x+0.05x^2+240 ?
The solutions to the equation (x)=-4x+0.05x^2+240 are x=50+10sqrt(23)i,x=50-10sqrt(23)i
Find the zeros of (x)=-4x+0.05x^2+240
The zeros of (x)=-4x+0.05x^2+240 are x=50+10sqrt(23)i,x=50-10sqrt(23)i