Solve sqrt{w-40}+sqrt{w}=10

$$\sqrt { w - 40 } + \sqrt { w } = 10$$

Solve for w

$$w=49$$

Solution Steps

Subtract \sqrt{w} from both sides of the equation.

$$\sqrt{w-40}=10-\sqrt{w}$$

Square both sides of the equation.

$$\left(\sqrt{w-40}\right)^{2}=\left(10-\sqrt{w}\right)^{2}$$

Calculate \sqrt{w-40} to the power of 2 and get w-40.

$$w-40=\left(10-\sqrt{w}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-\sqrt{w}\right)^{2}.

$$w-40=100-20\sqrt{w}+\left(\sqrt{w}\right)^{2}$$

Calculate \sqrt{w} to the power of 2 and get w.

$$w-40=100-20\sqrt{w}+w$$

Add 20\sqrt{w} to both sides.

$$w-40+20\sqrt{w}=100+w$$

Subtract w from both sides.

$$w-40+20\sqrt{w}-w=100$$

Combine w and -w to get 0.

$$-40+20\sqrt{w}=100$$

Add 40 to both sides.

$$20\sqrt{w}=100+40$$

Add 100 and 40 to get 140.

$$20\sqrt{w}=140$$

Divide both sides by 20.

$$\sqrt{w}=\frac{140}{20}$$

Divide 140 by 20 to get 7.

$$\sqrt{w}=7$$

Square both sides of the equation.

$$w=49$$

Substitute 49 for w in the equation \sqrt{w-40}+\sqrt{w}=10.

$$\sqrt{49-40}+\sqrt{49}=10$$

Simplify. The value w=49 satisfies the equation.

$$10=10$$

Equation \sqrt{w-40}=-\sqrt{w}+10 has a unique solution.

$$w=49$$