Solve (A):P(A)=1:2,f

$$( A ) : P ( A ) = 1 : 2 , f$$

Solve for P

$$P=2A^{2}$$

$$A\neq 0$$

Solution Steps

Variable P cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2P, the least common multiple of P,2.

$$2AA=P$$

Multiply A and A to get A^{2}.

$$2A^{2}=P$$

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

$$P=2A^{2}$$

Variable P cannot be equal to 0.

$$P=2A^{2}\text{, }P\neq 0$$

Solve for A

$$A=\frac{\sqrt{2P}}{2}$$

$$A=-\frac{\sqrt{2P}}{2}\text{, }P>0$$