What are the solutions to the equation 7000-2x=0.01x^2+2x+1000 ?

The solutions to the equation 7000-2x=0.01x^2+2x+1000 are x=600,x=-1000

Find the zeros of 7000-2x=0.01x^2+2x+1000

The zeros of 7000-2x=0.01x^2+2x+1000 are x=600,x=-1000

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7000 - 2 x = 0.01 x^{2} + 2 x + 1000

x = 600, x = - 1000

Solution steps

7000 - 2 x = 0.01 x^{2} + 2 x + 1000

Multiply both sides by

100

700000 - 200 x = x^{2} + 200 x + 100000

Switch sides

x^{2} + 200 x + 100000 = 700000 - 200 x

Move

200 x

to the left side

x^{2} + 400 x + 100000 = 700000

Move

700000

to the left side

x^{2} + 400 x - 600000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 400 \pm 40 0 ^{2} - 4 \cdot 1 \cdot ( - 600000 )}{2 \cdot 1}

40 0^{2} - 4 \cdot 1 \cdot (- 600000) = 1600

x_{1, 2} = \frac{- 400 \pm 1600}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 400 + 1600}{2 \cdot 1}, x_{2} = \frac{- 400 - 1600}{2 \cdot 1}

x = \frac{- 400 + 1600}{2 \cdot 1} : 600

x = \frac{- 400 - 1600}{2 \cdot 1} : - 1000

The solutions to the quadratic equation are:

x = 600, x = - 1000

x, y x^{2} - 25 y - x = 0

5 x^{2} - 20 x = 15

s^{2} + 60 s + 150 = 0

- 2 x^{2} + 11 x + 30 = 0

x^{2} + 8 x = 9

What are the solutions to the equation 7000-2x=0.01x^2+2x+1000 ?
The solutions to the equation 7000-2x=0.01x^2+2x+1000 are x=600,x=-1000
Find the zeros of 7000-2x=0.01x^2+2x+1000
The zeros of 7000-2x=0.01x^2+2x+1000 are x=600,x=-1000