Solve a^2=20^2+30^2-2*20*30*1/2

$$a ^ { 2 } = 20 ^ { 2 } + 30 ^ { 2 } - 2 \times 20 \times 30 \times \frac { 1 } { 2 }$$

Solve for a

$$a=10\sqrt{7}\approx 26.457513111$$

$$a=-10\sqrt{7}\approx -26.457513111$$

Steps by Finding Square Root

Calculate 20 to the power of 2 and get 400.

$$a^{2}=400+30^{2}-2\times 20\times 30\times \frac{1}{2}$$

Calculate 30 to the power of 2 and get 900.

$$a^{2}=400+900-2\times 20\times 30\times \frac{1}{2}$$

Add 400 and 900 to get 1300.

$$a^{2}=1300-2\times 20\times 30\times \frac{1}{2}$$

Multiply 2 and 20 to get 40.

$$a^{2}=1300-40\times 30\times \frac{1}{2}$$

Multiply 40 and 30 to get 1200.

$$a^{2}=1300-1200\times \frac{1}{2}$$

Multiply 1200 and \frac{1}{2} to get 600.

$$a^{2}=1300-600$$

Subtract 600 from 1300 to get 700.

$$a^{2}=700$$

Take the square root of both sides of the equation.

$$a=10\sqrt{7} a=-10\sqrt{7}$$

Steps Using the Quadratic Formula

Calculate 20 to the power of 2 and get 400.

$$a^{2}=400+30^{2}-2\times 20\times 30\times \frac{1}{2}$$

Calculate 30 to the power of 2 and get 900.

$$a^{2}=400+900-2\times 20\times 30\times \frac{1}{2}$$

Add 400 and 900 to get 1300.

$$a^{2}=1300-2\times 20\times 30\times \frac{1}{2}$$

Multiply 2 and 20 to get 40.

$$a^{2}=1300-40\times 30\times \frac{1}{2}$$

Multiply 40 and 30 to get 1200.

$$a^{2}=1300-1200\times \frac{1}{2}$$

Multiply 1200 and \frac{1}{2} to get 600.

$$a^{2}=1300-600$$

Subtract 600 from 1300 to get 700.

$$a^{2}=700$$

Subtract 700 from both sides.

$$a^{2}-700=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -700 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-700\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-700\right)}}{2}$$

Multiply -4 times -700.

$$a=\frac{0±\sqrt{2800}}{2}$$

Take the square root of 2800.

$$a=\frac{0±20\sqrt{7}}{2}$$

Now solve the equation a=\frac{0±20\sqrt{7}}{2} when ± is plus.

$$a=10\sqrt{7}$$

Now solve the equation a=\frac{0±20\sqrt{7}}{2} when ± is minus.

$$a=-10\sqrt{7}$$

The equation is now solved.

$$a=10\sqrt{7} a=-10\sqrt{7}$$