What are the solutions to the equation 1/9 y^2=y+1/36 ?

The solutions to the equation 1/9 y^2=y+1/36 are y=(9+sqrt(82))/2 ,y=(9-sqrt(82))/2

Find the zeros of 1/9 y^2=y+1/36

The zeros of 1/9 y^2=y+1/36 are y=(9+sqrt(82))/2 ,y=(9-sqrt(82))/2

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\frac{1}{9} y^{2} = y + \frac{1}{36}

y = \frac{9 + 82}{2}, y = \frac{9 - 82}{2}

Decimal Notation

y = 9.02769 \dots, y = - 0.02769 \dots

Solution steps

\frac{1}{9} y^{2} = y + \frac{1}{36}

Find Least Common Multiplier of

9, 36 : 36

Multiply by LCM=

36

\frac{1}{9} y^{2} \cdot 36 = y \cdot 36 + \frac{1}{36} \cdot 36

Simplify

4 y^{2} = 36 y + 1

Move

1

to the left side

4 y^{2} - 1 = 36 y

Move

36 y

to the left side

4 y^{2} - 1 - 36 y = 0

Write in the standard form

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

4 y^{2} - 36 y - 1 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 36 ) \pm ( - 36 ) ^{2} - 4 \cdot 4 ( - 1 )}{2 \cdot 4}

(- 36)^{2} - 4 \cdot 4 (- 1) = 482

y_{1, 2} = \frac{- ( - 36 ) \pm 4 82}{2 \cdot 4}

Separate the solutions

y_{1} = \frac{- ( - 36 ) + 4 82}{2 \cdot 4}, y_{2} = \frac{- ( - 36 ) - 4 82}{2 \cdot 4}

y = \frac{- ( - 36 ) + 4 82}{2 \cdot 4} : \frac{9 + 82}{2}

y = \frac{- ( - 36 ) - 4 82}{2 \cdot 4} : \frac{9 - 82}{2}

The solutions to the quadratic equation are:

y = \frac{9 + 82}{2}, y = \frac{9 - 82}{2}

2 x^{2} - 8 x = 12

4 x = 60

- 161

0.2 5^{- 2}

12 + 27

What are the solutions to the equation 1/9 y^2=y+1/36 ?
The solutions to the equation 1/9 y^2=y+1/36 are y=(9+sqrt(82))/2 ,y=(9-sqrt(82))/2
Find the zeros of 1/9 y^2=y+1/36
The zeros of 1/9 y^2=y+1/36 are y=(9+sqrt(82))/2 ,y=(9-sqrt(82))/2