Solve a^2+a^2=(11sqrt{2})^2

$$a ^ { 2 } + a ^ { 2 } = ( 11 \sqrt { 2 } ) ^ { 2 }$$

Solve for a

$$a=11$$

$$a=-11$$

Steps Using Difference of Squares

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

$$2a^{2}=\left(11\sqrt{2}\right)^{2}$$

Expand \left(11\sqrt{2}\right)^{2}.

$$2a^{2}=11^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$2a^{2}=121\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2a^{2}=121\times 2$$

Multiply 121 and 2 to get 242.

$$2a^{2}=242$$

Subtract 242 from both sides.

$$2a^{2}-242=0$$

Divide both sides by 2.

$$a^{2}-121=0$$

Consider a^{2}-121. Rewrite a^{2}-121 as a^{2}-11^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-11\right)\left(a+11\right)=0$$

To find equation solutions, solve a-11=0 and a+11=0.

$$a=11 a=-11$$

Steps by Finding Square Root

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

$$2a^{2}=\left(11\sqrt{2}\right)^{2}$$

Expand \left(11\sqrt{2}\right)^{2}.

$$2a^{2}=11^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$2a^{2}=121\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2a^{2}=121\times 2$$

Multiply 121 and 2 to get 242.

$$2a^{2}=242$$

Divide both sides by 2.

$$a^{2}=\frac{242}{2}$$

Divide 242 by 2 to get 121.

$$a^{2}=121$$

Take the square root of both sides of the equation.

$$a=11 a=-11$$

Steps Using the Quadratic Formula

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

$$2a^{2}=\left(11\sqrt{2}\right)^{2}$$

Expand \left(11\sqrt{2}\right)^{2}.

$$2a^{2}=11^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$2a^{2}=121\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2a^{2}=121\times 2$$

Multiply 121 and 2 to get 242.

$$2a^{2}=242$$

Subtract 242 from both sides.

$$2a^{2}-242=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -242 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-242\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-242\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-242\right)}}{2\times 2}$$

Multiply -8 times -242.

$$a=\frac{0±\sqrt{1936}}{2\times 2}$$

Take the square root of 1936.

$$a=\frac{0±44}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±44}{4}$$

Now solve the equation a=\frac{0±44}{4} when ± is plus. Divide 44 by 4.

$$a=11$$

Now solve the equation a=\frac{0±44}{4} when ± is minus. Divide -44 by 4.

$$a=-11$$

The equation is now solved.

$$a=11 a=-11$$