Solve sqrt{x^2-left(49-xright)^2}=7

$$\sqrt{ { x }^{ 2 } - { \left(49-x \right) }^{ 2 } } =7$$

Solve for x

$$x=25$$

Steps for Solving Radical Equations

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(49-x\right)^{2}.

$$\sqrt{x^{2}-\left(2401-98x+x^{2}\right)}=7$$

To find the opposite of 2401-98x+x^{2}, find the opposite of each term.

$$\sqrt{x^{2}-2401+98x-x^{2}}=7$$

Combine x^{2} and -x^{2} to get 0.

$$\sqrt{-2401+98x}=7$$

Square both sides of the equation.

$$98x-2401=49$$

Add 2401 to both sides of the equation.

$$98x-2401-\left(-2401\right)=49-\left(-2401\right)$$

Subtracting -2401 from itself leaves 0.

$$98x=49-\left(-2401\right)$$

Subtract -2401 from 49.

$$98x=2450$$

Divide both sides by 98.

$$\frac{98x}{98}=\frac{2450}{98}$$

Dividing by 98 undoes the multiplication by 98.

$$x=\frac{2450}{98}$$

Divide 2450 by 98.

$$x=25$$