What are the solutions to the equation (3r)^2=15^2-(r+(r+1))^2 ?

The solutions to the equation (3r)^2=15^2-(r+(r+1))^2 are r=-56/13 ,r=4

Find the zeros of (3r)^2=15^2-(r+(r+1))^2

The zeros of (3r)^2=15^2-(r+(r+1))^2 are r=-56/13 ,r=4

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(3 r)^{2} = 1 5^{2} - (r + (r + 1))^{2}

r = - \frac{56}{13}, r = 4

Decimal Notation

r = - 4.30769 \dots, r = 4

Solution steps

(3 r)^{2} = 1 5^{2} - (r + (r + 1))^{2}

Expand

(3 r)^{2} : 9 r^{2}

Expand

1 5^{2} - (r + (r + 1))^{2} : - 4 r^{2} - 4 r + 224

9 r^{2} = - 4 r^{2} - 4 r + 224

Switch sides

- 4 r^{2} - 4 r + 224 = 9 r^{2}

Move

9 r^{2}

to the left side

- 13 r^{2} - 4 r + 224 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 ( - 13 ) \cdot 224}{2 ( - 13 )}

(- 4)^{2} - 4 (- 13) \cdot 224 = 108

r_{1, 2} = \frac{- ( - 4 ) \pm 108}{2 ( - 13 )}

Separate the solutions

r_{1} = \frac{- ( - 4 ) + 108}{2 ( - 13 )}, r_{2} = \frac{- ( - 4 ) - 108}{2 ( - 13 )}

r = \frac{- ( - 4 ) + 108}{2 ( - 13 )} : - \frac{56}{13}

r = \frac{- ( - 4 ) - 108}{2 ( - 13 )} : 4

The solutions to the quadratic equation are:

r = - \frac{56}{13}, r = 4

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

y^{2} + 17 y + 16 = 0

x^{2} + 2 x + 50

\frac{6 ^{2}}{1 5 ^{2}} + \frac{x ^{2}}{1 0 ^{2}} = 1

104.607075 = 0.1775 x^{2} - 36.621 x + 2005.1

What are the solutions to the equation (3r)^2=15^2-(r+(r+1))^2 ?
The solutions to the equation (3r)^2=15^2-(r+(r+1))^2 are r=-56/13 ,r=4
Find the zeros of (3r)^2=15^2-(r+(r+1))^2
The zeros of (3r)^2=15^2-(r+(r+1))^2 are r=-56/13 ,r=4