Solve 28^2=14^2+a^2

$$28 ^ { 2 } = 14 ^ { 2 } + a ^ { 2 }$$

Solve for a

$$a=14\sqrt{3}\approx 24.248711306$$

$$a=-14\sqrt{3}\approx -24.248711306$$

Steps by Finding Square Root

Calculate 28 to the power of 2 and get 784.

$$784=14^{2}+a^{2}$$

Calculate 14 to the power of 2 and get 196.

$$784=196+a^{2}$$

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

$$196+a^{2}=784$$

Subtract 196 from both sides.

$$a^{2}=784-196$$

Subtract 196 from 784 to get 588.

$$a^{2}=588$$

Take the square root of both sides of the equation.

$$a=14\sqrt{3} a=-14\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate 28 to the power of 2 and get 784.

$$784=14^{2}+a^{2}$$

Calculate 14 to the power of 2 and get 196.

$$784=196+a^{2}$$

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

$$196+a^{2}=784$$

Subtract 784 from both sides.

$$196+a^{2}-784=0$$

Subtract 784 from 196 to get -588.

$$-588+a^{2}=0$$

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.

$$a^{2}-588=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -588 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-588\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-588\right)}}{2}$$

Multiply -4 times -588.

$$a=\frac{0±\sqrt{2352}}{2}$$

Take the square root of 2352.

$$a=\frac{0±28\sqrt{3}}{2}$$

Now solve the equation a=\frac{0±28\sqrt{3}}{2} when ± is plus.

$$a=14\sqrt{3}$$

Now solve the equation a=\frac{0±28\sqrt{3}}{2} when ± is minus.

$$a=-14\sqrt{3}$$

The equation is now solved.

$$a=14\sqrt{3} a=-14\sqrt{3}$$