Solve sqrt{5x-8}=sqrt{3x+22}

$$\sqrt { 5 x - 8 } = \sqrt { 3 x + 22 }$$

Solve for x

$$x=15$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{5x-8}\right)^{2}=\left(\sqrt{3x+22}\right)^{2}$$

Calculate \sqrt{5x-8} to the power of 2 and get 5x-8.

$$5x-8=\left(\sqrt{3x+22}\right)^{2}$$

Calculate \sqrt{3x+22} to the power of 2 and get 3x+22.

$$5x-8=3x+22$$

Subtract 3x from both sides.

$$5x-8-3x=22$$

Combine 5x and -3x to get 2x.

$$2x-8=22$$

Add 8 to both sides.

$$2x=22+8$$

Add 22 and 8 to get 30.

$$2x=30$$

Divide both sides by 2.

$$x=\frac{30}{2}$$

Divide 30 by 2 to get 15.

$$x=15$$

Substitute 15 for x in the equation \sqrt{5x-8}=\sqrt{3x+22}.

$$\sqrt{5\times 15-8}=\sqrt{3\times 15+22}$$

Simplify. The value x=15 satisfies the equation.

$$67^{\frac{1}{2}}=67^{\frac{1}{2}}$$

Equation \sqrt{5x-8}=\sqrt{3x+22} has a unique solution.

$$x=15$$