Solve 1/2(z+x)(x)=60

$$\frac { 1 } { 2 } ( z + x ) ( x ) = 60$$

Solve for z

$$z=-x+\frac{120}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by z+x.

$$\left(\frac{1}{2}z+\frac{1}{2}x\right)x=60$$

Use the distributive property to multiply \frac{1}{2}z+\frac{1}{2}x by x.

$$\frac{1}{2}zx+\frac{1}{2}x^{2}=60$$

Subtract \frac{1}{2}x^{2} from both sides.

$$\frac{1}{2}zx=60-\frac{1}{2}x^{2}$$

The equation is in standard form.

$$\frac{x}{2}z=-\frac{x^{2}}{2}+60$$

Divide both sides by \frac{1}{2}x.

$$\frac{2\times \frac{x}{2}z}{x}=\frac{2\left(-\frac{x^{2}}{2}+60\right)}{x}$$

Dividing by \frac{1}{2}x undoes the multiplication by \frac{1}{2}x.

$$z=\frac{2\left(-\frac{x^{2}}{2}+60\right)}{x}$$

Divide 60-\frac{x^{2}}{2} by \frac{1}{2}x.

$$z=-x+\frac{120}{x}$$

Solve for x

$$x=\frac{\sqrt{z^{2}+480}-z}{2}$$

$$x=\frac{-\sqrt{z^{2}+480}-z}{2}$$