What are the solutions to the equation 7000-2Q=0.1Q^2+2Q+1000 ?

The solutions to the equation 7000-2Q=0.1Q^2+2Q+1000 are Q=20(sqrt(151)-1),Q=-20(1+sqrt(151))

Find the zeros of 7000-2Q=0.1Q^2+2Q+1000

The zeros of 7000-2Q=0.1Q^2+2Q+1000 are Q=20(sqrt(151)-1),Q=-20(1+sqrt(151))

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7000 - 2 Q = 0.1 Q^{2} + 2 Q + 1000

Q = 20 (151 - 1), Q = - 20 (1 + 151)

Decimal Notation

Q = 225.76411 \dots, Q = - 265.76411 \dots

Solution steps

7000 - 2 Q = 0.1 Q^{2} + 2 Q + 1000

Multiply both sides by

10

70000 - 20 Q = Q^{2} + 20 Q + 10000

Switch sides

Q^{2} + 20 Q + 10000 = 70000 - 20 Q

Move

20 Q

to the left side

Q^{2} + 40 Q + 10000 = 70000

Move

70000

to the left side

Q^{2} + 40 Q - 60000 = 0

Solve with the quadratic formula

Q_{1, 2} = \frac{- 40 \pm 4 0 ^{2} - 4 \cdot 1 \cdot ( - 60000 )}{2 \cdot 1}

4 0^{2} - 4 \cdot 1 \cdot (- 60000) = 40151

Q_{1, 2} = \frac{- 40 \pm 40 151}{2 \cdot 1}

Separate the solutions

Q_{1} = \frac{- 40 + 40 151}{2 \cdot 1}, Q_{2} = \frac{- 40 - 40 151}{2 \cdot 1}

Q = \frac{- 40 + 40 151}{2 \cdot 1} : 20 (151 - 1)

Q = \frac{- 40 - 40 151}{2 \cdot 1} : - 20 (1 + 151)

The solutions to the quadratic equation are:

Q = 20 (151 - 1), Q = - 20 (1 + 151)

12 x - 0.24 x^{2} = 0

x^{2} + 8 x - 20

A, A^{2} - Y = CB

5 a^{2} = 45

d, h = - 0.13 d (d - 20)

What are the solutions to the equation 7000-2Q=0.1Q^2+2Q+1000 ?
The solutions to the equation 7000-2Q=0.1Q^2+2Q+1000 are Q=20(sqrt(151)-1),Q=-20(1+sqrt(151))
Find the zeros of 7000-2Q=0.1Q^2+2Q+1000
The zeros of 7000-2Q=0.1Q^2+2Q+1000 are Q=20(sqrt(151)-1),Q=-20(1+sqrt(151))