Solve 5*sqrt{2x-1}=sqrt{x+24}

$$5 \cdot \sqrt { 2 x - 1 } = \sqrt { x + 24 }$$

Solve for x

$$x=1$$

Solution Steps

Square both sides of the equation.

$$\left(5\sqrt{2x-1}\right)^{2}=\left(\sqrt{x+24}\right)^{2}$$

Expand \left(5\sqrt{2x-1}\right)^{2}.

$$5^{2}\left(\sqrt{2x-1}\right)^{2}=\left(\sqrt{x+24}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{2x-1}\right)^{2}=\left(\sqrt{x+24}\right)^{2}$$

Calculate \sqrt{2x-1} to the power of 2 and get 2x-1.

$$25\left(2x-1\right)=\left(\sqrt{x+24}\right)^{2}$$

Use the distributive property to multiply 25 by 2x-1.

$$50x-25=\left(\sqrt{x+24}\right)^{2}$$

Calculate \sqrt{x+24} to the power of 2 and get x+24.

$$50x-25=x+24$$

Subtract x from both sides.

$$50x-25-x=24$$

Combine 50x and -x to get 49x.

$$49x-25=24$$

Add 25 to both sides.

$$49x=24+25$$

Add 24 and 25 to get 49.

$$49x=49$$

Divide both sides by 49.

$$x=\frac{49}{49}$$

Divide 49 by 49 to get 1.

$$x=1$$

Substitute 1 for x in the equation 5\sqrt{2x-1}=\sqrt{x+24}.

$$5\sqrt{2\times 1-1}=\sqrt{1+24}$$

Simplify. The value x=1 satisfies the equation.

$$5=5$$

Equation 5\sqrt{2x-1}=\sqrt{x+24} has a unique solution.

$$x=1$$