Solve (a+5)*(a+5)=A+225

$$( a + 5 ) \cdot ( a + 5 ) = A + 225$$

Solve for A

$$A=\left(a-10\right)\left(a+20\right)$$

Solution Steps

Multiply a+5 and a+5 to get \left(a+5\right)^{2}.

$$\left(a+5\right)^{2}=A+225$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+5\right)^{2}.

$$a^{2}+10a+25=A+225$$

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

$$A+225=a^{2}+10a+25$$

Subtract 225 from both sides.

$$A=a^{2}+10a+25-225$$

Subtract 225 from 25 to get -200.

$$A=a^{2}+10a-200$$

Solve for a

$$a=-\left(\sqrt{A+225}+5\right)$$

$$a=\sqrt{A+225}-5\text{, }A\geq -225$$