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

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

Solve for a

$$a = \frac{5 \sqrt{2}}{2} \approx 3.535533906$$

$$a = -\frac{5 \sqrt{2}}{2} \approx -3.535533906$$

Steps by Finding Square Root

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

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

Calculate 5 to the power of 2 and get 25.

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

Divide both sides by 2.

$$a^{2}=\frac{25}{2}$$

Take the square root of both sides of the equation.

$$a=\frac{5\sqrt{2}}{2} a=-\frac{5\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

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

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

Calculate 5 to the power of 2 and get 25.

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

Subtract 25 from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-25\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-25\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-25\right)}}{2\times 2}$$

Multiply -8 times -25.

$$a=\frac{0±\sqrt{200}}{2\times 2}$$

Take the square root of 200.

$$a=\frac{0±10\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±10\sqrt{2}}{4}$$

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

$$a=\frac{5\sqrt{2}}{2}$$

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

$$a=-\frac{5\sqrt{2}}{2}$$

The equation is now solved.

$$a=\frac{5\sqrt{2}}{2} a=-\frac{5\sqrt{2}}{2}$$