Solve a^2+a^2=4^2

$$a ^ { 2 } + a ^ { 2 } = 4 ^ { 2 }$$

Solve for a

$$a=2\sqrt{2}\approx 2.828427125$$

$$a=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Combine a^{2} and a^{2} to get 2a^{2}.

$$2a^{2}=4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$2a^{2}=16$$

Divide both sides by 2.

$$a^{2}=\frac{16}{2}$$

Divide 16 by 2 to get 8.

$$a^{2}=8$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Combine a^{2} and a^{2} to get 2a^{2}.

$$2a^{2}=4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$2a^{2}=16$$

Subtract 16 from both sides.

$$2a^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-16\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-16\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-16\right)}}{2\times 2}$$

Multiply -8 times -16.

$$a=\frac{0±\sqrt{128}}{2\times 2}$$

Take the square root of 128.

$$a=\frac{0±8\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±8\sqrt{2}}{4}$$

Now solve the equation a=\frac{0±8\sqrt{2}}{4} when ± is plus.

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

Now solve the equation a=\frac{0±8\sqrt{2}}{4} when ± is minus.

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

The equation is now solved.

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