What are the solutions to the equation 9000+25x+1/2 x^2=(255-1/2 x)x ?

The solutions to the equation 9000+25x+1/2 x^2=(255-1/2 x)x are x=180,x=50

Find the zeros of 9000+25x+1/2 x^2=(255-1/2 x)x

The zeros of 9000+25x+1/2 x^2=(255-1/2 x)x are x=180,x=50

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9000 + 25 x + \frac{1}{2} x^{2} = (255 - \frac{1}{2} x) x

x = 180, x = 50

Solution steps

9000 + 25 x + \frac{1}{2} x^{2} = (255 - \frac{1}{2} x) x

Multiply both sides by

2

18000 + 50 x + x^{2} = 2 x (255 - \frac{1}{2} x)

Expand

2 x (255 - \frac{1}{2} x) : 510 x - x^{2}

18000 + 50 x + x^{2} = 510 x - x^{2}

Move

x^{2}

to the left side

18000 + 50 x + 2 x^{2} = 510 x

Move

510 x

to the left side

2 x^{2} - 460 x + 18000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 460 ) \pm ( - 460 ) ^{2} - 4 \cdot 2 \cdot 18000}{2 \cdot 2}

(- 460)^{2} - 4 \cdot 2 \cdot 18000 = 260

x_{1, 2} = \frac{- ( - 460 ) \pm 260}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 460 ) + 260}{2 \cdot 2}, x_{2} = \frac{- ( - 460 ) - 260}{2 \cdot 2}

x = \frac{- ( - 460 ) + 260}{2 \cdot 2} : 180

x = \frac{- ( - 460 ) - 260}{2 \cdot 2} : 50

The solutions to the quadratic equation are:

x = 180, x = 50

21 x^{2} + 95 = 0

(2 x - 6) (x - 4) (4) = 72

x^{2} + 32 x + 256 = 0

0 = - x^{2} + 4 x - 3

(x + 2)^{2} = \frac{3}{2}

What are the solutions to the equation 9000+25x+1/2 x^2=(255-1/2 x)x ?
The solutions to the equation 9000+25x+1/2 x^2=(255-1/2 x)x are x=180,x=50
Find the zeros of 9000+25x+1/2 x^2=(255-1/2 x)x
The zeros of 9000+25x+1/2 x^2=(255-1/2 x)x are x=180,x=50