Solve a^2+a^2=10

$$a ^ { 2 } + a ^ { 2 } = 10$$

Solve for a

$$a=\sqrt{5}\approx 2.236067977$$

$$a=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

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

$$2a^{2}=10$$

Divide both sides by 2.

$$a^{2}=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$a^{2}=5$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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

$$2a^{2}=10$$

Subtract 10 from both sides.

$$2a^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-10\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-10\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-10\right)}}{2\times 2}$$

Multiply -8 times -10.

$$a=\frac{0±\sqrt{80}}{2\times 2}$$

Take the square root of 80.

$$a=\frac{0±4\sqrt{5}}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±4\sqrt{5}}{4}$$

Now solve the equation a=\frac{0±4\sqrt{5}}{4} when ± is plus.

$$a=\sqrt{5}$$

Now solve the equation a=\frac{0±4\sqrt{5}}{4} when ± is minus.

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

The equation is now solved.

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