What are the solutions to the equation x^2+(1/9 x^2-20x+900)=1620 ?

The solutions to the equation x^2+(1/9 x^2-20x+900)=1620 are x=36,x=-18

Find the zeros of x^2+(1/9 x^2-20x+900)=1620

The zeros of x^2+(1/9 x^2-20x+900)=1620 are x=36,x=-18

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x^{2} + (\frac{1}{9} x^{2} - 20 x + 900) = 1620

x = 36, x = - 18

Solution steps

x^{2} + (\frac{1}{9} x^{2} - 20 x + 900) = 1620

Expand

x^{2} + (\frac{1}{9} x^{2} - 20 x + 900) : \frac{10}{9} x^{2} - 20 x + 900

\frac{10}{9} x^{2} - 20 x + 900 = 1620

Move

1620

to the left side

\frac{10}{9} x^{2} - 20 x - 720 = 0

Write in the standard form

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

\frac{10 x ^{2}}{9} - 20 x - 720 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot \frac{10}{9} ( - 720 )}{2 \cdot \frac{10}{9}}

(- 20)^{2} - 4 \cdot \frac{10}{9} (- 720) = 60

x_{1, 2} = \frac{- ( - 20 ) \pm 60}{2 \cdot \frac{10}{9}}

Separate the solutions

x_{1} = \frac{- ( - 20 ) + 60}{2 \cdot \frac{10}{9}}, x_{2} = \frac{- ( - 20 ) - 60}{2 \cdot \frac{10}{9}}

x = \frac{- ( - 20 ) + 60}{2 \frac{10}{9}} : 36

x = \frac{- ( - 20 ) - 60}{2 \frac{10}{9}} : - 18

The solutions to the quadratic equation are:

x = 36, x = - 18

9 x^{2} - 26 x - 3

63 ab - 2 1^{2} - 42 b + 14 a

6 (2 y + 3) + 4 = 2 (2 y - 5) + 13

x^{2} - 2 x > 8

16 x^{2} - 24 x - 91 = 0

What are the solutions to the equation x^2+(1/9 x^2-20x+900)=1620 ?
The solutions to the equation x^2+(1/9 x^2-20x+900)=1620 are x=36,x=-18
Find the zeros of x^2+(1/9 x^2-20x+900)=1620
The zeros of x^2+(1/9 x^2-20x+900)=1620 are x=36,x=-18