Solve sqrt{11x-8}=sqrt{x+3}

$$\sqrt { 11 x - 8 } = \sqrt { x + 3 }$$

Solve for x

$$x = \frac{11}{10} = 1\frac{1}{10} = 1.1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{11x-8}\right)^{2}=\left(\sqrt{x+3}\right)^{2}$$

Calculate \sqrt{11x-8} to the power of 2 and get 11x-8.

$$11x-8=\left(\sqrt{x+3}\right)^{2}$$

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

$$11x-8=x+3$$

Subtract x from both sides.

$$11x-8-x=3$$

Combine 11x and -x to get 10x.

$$10x-8=3$$

Add 8 to both sides.

$$10x=3+8$$

Add 3 and 8 to get 11.

$$10x=11$$

Divide both sides by 10.

$$x=\frac{11}{10}$$

Substitute \frac{11}{10} for x in the equation \sqrt{11x-8}=\sqrt{x+3}.

$$\sqrt{11\times \frac{11}{10}-8}=\sqrt{\frac{11}{10}+3}$$

Simplify. The value x=\frac{11}{10} satisfies the equation.

$$\frac{1}{10}\times 410^{\frac{1}{2}}=\frac{1}{10}\times 410^{\frac{1}{2}}$$

Equation \sqrt{11x-8}=\sqrt{x+3} has a unique solution.

$$x=\frac{11}{10}$$