What are the solutions to the equation 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi ?

The solutions to the equation 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi are r= 9/2 ,r=-9/2

Find the zeros of 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi

The zeros of 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi are r= 9/2 ,r=-9/2

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\frac{1}{8} (5 r)^{2} π - π (3 r)^{2} \frac{1}{8} = \frac{81}{2} π

r = \frac{9}{2}, r = - \frac{9}{2}

Decimal Notation

r = 4.5, r = - 4.5

Solution steps

\frac{1}{8} (5 r)^{2} π - π (3 r)^{2} \frac{1}{8} = \frac{81}{2} π

Find Least Common Multiplier of

8, 2 : 8

Multiply by LCM=

8

\frac{1}{8} (5 r)^{2} π 8 - π (3 r)^{2} \frac{1}{8} \cdot 8 = \frac{81}{2} π 8

Simplify

25 π r^{2} - 9 π r^{2} = 324 π

16 π r^{2} = 324 π

Move

324 π

to the left side

16 π r^{2} - 324 π = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 \cdot 16 π ( - 324 π )}{2 \cdot 16 π}

0^{2} - 4 \cdot 16 π (- 324 π) = 144 π

r_{1, 2} = \frac{- 0 \pm 144 π}{2 \cdot 16 π}

Separate the solutions

r_{1} = \frac{- 0 + 144 π}{2 \cdot 16 π}, r_{2} = \frac{- 0 - 144 π}{2 \cdot 16 π}

r = \frac{- 0 + 144 π}{2 \cdot 16 π} : \frac{9}{2}

r = \frac{- 0 - 144 π}{2 \cdot 16 π} : - \frac{9}{2}

The solutions to the quadratic equation are:

r = \frac{9}{2}, r = - \frac{9}{2}

x, x^{2} + m^{2} = 0

2 x^{2} + 4 x + 4 = 100

5 x^{2} - 16 x = 0

X^{2} + X + 2 = 0

3 x^{2} = - 2 x + 6

What are the solutions to the equation 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi ?
The solutions to the equation 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi are r= 9/2 ,r=-9/2
Find the zeros of 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi
The zeros of 1/8 (5r)^2pi-pi(3r)^2 1/8 = 81/2 pi are r= 9/2 ,r=-9/2