Solve sqrt{left(12+xright)^2-x^2}=16*16

$$\sqrt{ { \left(12+x \right) }^{ 2 } - { x }^{ 2 } } =16 \times 16$$

Solve for x

$$x = \frac{8174}{3} = 2724\frac{2}{3} \approx 2724.666666667$$

Steps for Solving Radical Equations

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(12+x\right)^{2}.

$$\sqrt{144+24x+x^{2}-x^{2}}=16\times 16$$

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

$$\sqrt{144+24x}=16\times 16$$

Multiply 16 and 16 to get 256.

$$\sqrt{144+24x}=256$$

Square both sides of the equation.

$$24x+144=65536$$

Subtract 144 from both sides of the equation.

$$24x+144-144=65536-144$$

Subtracting 144 from itself leaves 0.

$$24x=65536-144$$

Subtract 144 from 65536.

$$24x=65392$$

Divide both sides by 24.

$$\frac{24x}{24}=\frac{65392}{24}$$

Dividing by 24 undoes the multiplication by 24.

$$x=\frac{65392}{24}$$

Reduce the fraction \frac{65392}{24} to lowest terms by extracting and canceling out 8.

$$x=\frac{8174}{3}$$