Solve a^2+3^2=7^2

$$a ^ { 2 } + 3 ^ { 2 } = 7 ^ { 2 }$$

Solve for a

$$a=2\sqrt{10}\approx 6.32455532$$

$$a=-2\sqrt{10}\approx -6.32455532$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$a^{2}+9=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$a^{2}+9=49$$

Subtract 9 from both sides.

$$a^{2}=49-9$$

Subtract 9 from 49 to get 40.

$$a^{2}=40$$

Take the square root of both sides of the equation.

$$a=2\sqrt{10} a=-2\sqrt{10}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$a^{2}+9=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$a^{2}+9=49$$

Subtract 49 from both sides.

$$a^{2}+9-49=0$$

Subtract 49 from 9 to get -40.

$$a^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-40\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-40\right)}}{2}$$

Multiply -4 times -40.

$$a=\frac{0±\sqrt{160}}{2}$$

Take the square root of 160.

$$a=\frac{0±4\sqrt{10}}{2}$$

Now solve the equation a=\frac{0±4\sqrt{10}}{2} when ± is plus.

$$a=2\sqrt{10}$$

Now solve the equation a=\frac{0±4\sqrt{10}}{2} when ± is minus.

$$a=-2\sqrt{10}$$

The equation is now solved.

$$a=2\sqrt{10} a=-2\sqrt{10}$$