Solve 48=a^2+1/2a4

$$48 = a ^ { 2 } + \frac { 1 } { 2 } a 4$$

Solve for a_4

$$a_{4}=96-2a^{2}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a^{2}+\frac{1}{2}a_{4}=48$$

Subtract a^{2} from both sides.

$$\frac{1}{2}a_{4}=48-a^{2}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}a_{4}}{\frac{1}{2}}=\frac{48-a^{2}}{\frac{1}{2}}$$

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

$$a_{4}=\frac{48-a^{2}}{\frac{1}{2}}$$

Divide -a^{2}+48 by \frac{1}{2} by multiplying -a^{2}+48 by the reciprocal of \frac{1}{2}.

$$a_{4}=96-2a^{2}$$

Solve for a

$$a=\frac{\sqrt{192-2a_{4}}}{2}$$

$$a=-\frac{\sqrt{192-2a_{4}}}{2}\text{, }a_{4}\leq 96$$