What are the solutions to the equation 200=1.1x+0.06x^2 ?

The solutions to the equation 200=1.1x+0.06x^2 are x=(5(sqrt(4921)-11))/6 ,x=-(5(11+sqrt(4921)))/6

Find the zeros of 200=1.1x+0.06x^2

The zeros of 200=1.1x+0.06x^2 are x=(5(sqrt(4921)-11))/6 ,x=-(5(11+sqrt(4921)))/6

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200 = 1.1 x + 0.06 x^{2}

x = \frac{5 ( 4921 - 11 )}{6}, x = - \frac{5 ( 11 + 4921 )}{6}

Decimal Notation

x = 49.29153 \dots, x = - 67.62486 \dots

Solution steps

200 = 1.1 x + 0.06 x^{2}

Multiply both sides by

100

20000 = 110 x + 6 x^{2}

Switch sides

110 x + 6 x^{2} = 20000

Move

20000

to the left side

110 x + 6 x^{2} - 20000 = 0

Write in the standard form

a x^{2} + b x + c = 0

6 x^{2} + 110 x - 20000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 110 \pm 11 0 ^{2} - 4 \cdot 6 ( - 20000 )}{2 \cdot 6}

11 0^{2} - 4 \cdot 6 (- 20000) = 104921

x_{1, 2} = \frac{- 110 \pm 10 4921}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- 110 + 10 4921}{2 \cdot 6}, x_{2} = \frac{- 110 - 10 4921}{2 \cdot 6}

x = \frac{- 110 + 10 4921}{2 \cdot 6} : \frac{5 ( 4921 - 11 )}{6}

x = \frac{- 110 - 10 4921}{2 \cdot 6} : - \frac{5 ( 11 + 4921 )}{6}

The solutions to the quadratic equation are:

x = \frac{5 ( 4921 - 11 )}{6}, x = - \frac{5 ( 11 + 4921 )}{6}

5 x^{2} - 2 x - 3 = 0

5 x^{2} + 6 x

2 x - 2 = 14

m^{2} + 18 m = - 9

0 \geq \frac{1}{2} x - 4 > 6

What are the solutions to the equation 200=1.1x+0.06x^2 ?
The solutions to the equation 200=1.1x+0.06x^2 are x=(5(sqrt(4921)-11))/6 ,x=-(5(11+sqrt(4921)))/6
Find the zeros of 200=1.1x+0.06x^2
The zeros of 200=1.1x+0.06x^2 are x=(5(sqrt(4921)-11))/6 ,x=-(5(11+sqrt(4921)))/6