Solve sqrt{4x+1}=sqrt{x+10}

$$\sqrt{ 4x+1 } = \sqrt{ x+10 }$$

Solve for x

$$x=3$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{4x+1}\right)^{2}=\left(\sqrt{x+10}\right)^{2}$$

Calculate \sqrt{4x+1} to the power of 2 and get 4x+1.

$$4x+1=\left(\sqrt{x+10}\right)^{2}$$

Calculate \sqrt{x+10} to the power of 2 and get x+10.

$$4x+1=x+10$$

Subtract x from both sides.

$$4x+1-x=10$$

Combine 4x and -x to get 3x.

$$3x+1=10$$

Subtract 1 from both sides.

$$3x=10-1$$

Subtract 1 from 10 to get 9.

$$3x=9$$

Divide both sides by 3.

$$x=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x=3$$

Substitute 3 for x in the equation \sqrt{4x+1}=\sqrt{x+10}.

$$\sqrt{4\times 3+1}=\sqrt{3+10}$$

Simplify. The value x=3 satisfies the equation.

$$13^{\frac{1}{2}}=13^{\frac{1}{2}}$$

Equation \sqrt{4x+1}=\sqrt{x+10} has a unique solution.

$$x=3$$