Solve sqrt{25x-6}=4sqrt{x+3}

$$\sqrt { 25 x - 6 } = 4 \sqrt { x + 3 }$$

Solve for x

$$x=6$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{25x-6}\right)^{2}=\left(4\sqrt{x+3}\right)^{2}$$

Calculate \sqrt{25x-6} to the power of 2 and get 25x-6.

$$25x-6=\left(4\sqrt{x+3}\right)^{2}$$

Expand \left(4\sqrt{x+3}\right)^{2}.

$$25x-6=4^{2}\left(\sqrt{x+3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$25x-6=16\left(\sqrt{x+3}\right)^{2}$$

Calculate \sqrt{x+3} to the power of 2 and get x+3.

$$25x-6=16\left(x+3\right)$$

Use the distributive property to multiply 16 by x+3.

$$25x-6=16x+48$$

Subtract 16x from both sides.

$$25x-6-16x=48$$

Combine 25x and -16x to get 9x.

$$9x-6=48$$

Add 6 to both sides.

$$9x=48+6$$

Add 48 and 6 to get 54.

$$9x=54$$

Divide both sides by 9.

$$x=\frac{54}{9}$$

Divide 54 by 9 to get 6.

$$x=6$$

Substitute 6 for x in the equation \sqrt{25x-6}=4\sqrt{x+3}.

$$\sqrt{25\times 6-6}=4\sqrt{6+3}$$

Simplify. The value x=6 satisfies the equation.

$$12=12$$

Equation \sqrt{25x-6}=4\sqrt{x+3} has a unique solution.

$$x=6$$