Solve 5^2=1^2+a^2

$$5 ^ { 2 } = 1 ^ { 2 } + a ^ { 2 }$$

Solve for a

$$a=2\sqrt{6}\approx 4.898979486$$

$$a=-2\sqrt{6}\approx -4.898979486$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25=1^{2}+a^{2}$$

Calculate 1 to the power of 2 and get 1.

$$25=1+a^{2}$$

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

$$1+a^{2}=25$$

Subtract 1 from both sides.

$$a^{2}=25-1$$

Subtract 1 from 25 to get 24.

$$a^{2}=24$$

Take the square root of both sides of the equation.

$$a=2\sqrt{6} a=-2\sqrt{6}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25=1^{2}+a^{2}$$

Calculate 1 to the power of 2 and get 1.

$$25=1+a^{2}$$

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

$$1+a^{2}=25$$

Subtract 25 from both sides.

$$1+a^{2}-25=0$$

Subtract 25 from 1 to get -24.

$$-24+a^{2}=0$$

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.

$$a^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-24\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-24\right)}}{2}$$

Multiply -4 times -24.

$$a=\frac{0±\sqrt{96}}{2}$$

Take the square root of 96.

$$a=\frac{0±4\sqrt{6}}{2}$$

Now solve the equation a=\frac{0±4\sqrt{6}}{2} when ± is plus.

$$a=2\sqrt{6}$$

Now solve the equation a=\frac{0±4\sqrt{6}}{2} when ± is minus.

$$a=-2\sqrt{6}$$

The equation is now solved.

$$a=2\sqrt{6} a=-2\sqrt{6}$$