Solve (x-24/5)^2+(18/5)^2=x^2-36

$$( x - \frac { 24 } { 5 } ) ^ { 2 } + ( \frac { 18 } { 5 } ) ^ { 2 } = x ^ { 2 } - 36$$

Solve for x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{24}{5}\right)^{2}.

$$x^{2}-\frac{48}{5}x+\frac{576}{25}+\left(\frac{18}{5}\right)^{2}=x^{2}-36$$

Calculate \frac{18}{5} to the power of 2 and get \frac{324}{25}.

$$x^{2}-\frac{48}{5}x+\frac{576}{25}+\frac{324}{25}=x^{2}-36$$

Add \frac{576}{25} and \frac{324}{25} to get 36.

$$x^{2}-\frac{48}{5}x+36=x^{2}-36$$

Subtract x^{2} from both sides.

$$x^{2}-\frac{48}{5}x+36-x^{2}=-36$$

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

$$-\frac{48}{5}x+36=-36$$

Subtract 36 from both sides.

$$-\frac{48}{5}x=-36-36$$

Subtract 36 from -36 to get -72.

$$-\frac{48}{5}x=-72$$

Multiply both sides by -\frac{5}{48}, the reciprocal of -\frac{48}{5}.

$$x=-72\left(-\frac{5}{48}\right)$$

Multiply -72 and -\frac{5}{48} to get \frac{15}{2}.

$$x=\frac{15}{2}$$