Solve 6y+69y=545sqrt{9y}

$$6y+69y = 545 \sqrt{ 9y }$$

Solve for y

$$y = \frac{11881}{25} = 475\frac{6}{25} = 475.24$$

$$y=0$$

Solution Steps

Square both sides of the equation.

$$\left(6y+69y\right)^{2}=\left(545\sqrt{9y}\right)^{2}$$

Combine 6y and 69y to get 75y.

$$\left(75y\right)^{2}=\left(545\sqrt{9y}\right)^{2}$$

Expand \left(75y\right)^{2}.

$$75^{2}y^{2}=\left(545\sqrt{9y}\right)^{2}$$

Calculate 75 to the power of 2 and get 5625.

$$5625y^{2}=\left(545\sqrt{9y}\right)^{2}$$

Expand \left(545\sqrt{9y}\right)^{2}.

$$5625y^{2}=545^{2}\left(\sqrt{9y}\right)^{2}$$

Calculate 545 to the power of 2 and get 297025.

$$5625y^{2}=297025\left(\sqrt{9y}\right)^{2}$$

Calculate \sqrt{9y} to the power of 2 and get 9y.

$$5625y^{2}=297025\times 9y$$

Multiply 297025 and 9 to get 2673225.

$$5625y^{2}=2673225y$$

Subtract 2673225y from both sides.

$$5625y^{2}-2673225y=0$$

Factor out y.

$$y\left(5625y-2673225\right)=0$$

To find equation solutions, solve y=0 and 5625y-2673225=0.

$$y=0 y=\frac{11881}{25}$$

Substitute 0 for y in the equation 6y+69y=545\sqrt{9y}.

$$6\times 0+69\times 0=545\sqrt{9\times 0}$$

Simplify. The value y=0 satisfies the equation.

$$0=0$$

Substitute \frac{11881}{25} for y in the equation 6y+69y=545\sqrt{9y}.

$$6\times \frac{11881}{25}+69\times \frac{11881}{25}=545\sqrt{9\times \frac{11881}{25}}$$

Simplify. The value y=\frac{11881}{25} satisfies the equation.

$$35643=35643$$

List all solutions of 6y+69y=545\sqrt{9y}.

$$y=0 y=\frac{11881}{25}$$