Solve 225=625+a^2

$$225 = 625 + a ^ { 2 }$$

Solve for a

$$a=-20i$$

$$a=20i$$

Steps by Finding Square Root

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

$$625+a^{2}=225$$

Subtract 625 from both sides.

$$a^{2}=225-625$$

Subtract 625 from 225 to get -400.

$$a^{2}=-400$$

The equation is now solved.

$$a=20i a=-20i$$

Steps Using the Quadratic Formula

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

$$625+a^{2}=225$$

Subtract 225 from both sides.

$$625+a^{2}-225=0$$

Subtract 225 from 625 to get 400.

$$400+a^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$a^{2}+400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 400}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 400}}{2}$$

Multiply -4 times 400.

$$a=\frac{0±\sqrt{-1600}}{2}$$

Take the square root of -1600.

$$a=\frac{0±40i}{2}$$

Now solve the equation a=\frac{0±40i}{2} when ± is plus.

$$a=20i$$

Now solve the equation a=\frac{0±40i}{2} when ± is minus.

$$a=-20i$$

The equation is now solved.

$$a=20i a=-20i$$