Solve a^2+a^2=16.97^2

$$a ^ { 2 } + a ^ { 2 } = 16.97 ^ { 2 }$$

Solve for a

$$a = \frac{1697 \sqrt{2}}{200} \approx 11.999602077$$

$$a = -\frac{1697 \sqrt{2}}{200} \approx -11.999602077$$

Steps by Finding Square Root

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

$$2a^{2}=16.97^{2}$$

Calculate 16.97 to the power of 2 and get 287.9809.

$$2a^{2}=287.9809$$

Divide both sides by 2.

$$a^{2}=\frac{287.9809}{2}$$

Expand \frac{287.9809}{2} by multiplying both numerator and the denominator by 10000.

$$a^{2}=\frac{2879809}{20000}$$

Take the square root of both sides of the equation.

$$a=\frac{1697\sqrt{2}}{200} a=-\frac{1697\sqrt{2}}{200}$$

Steps Using the Quadratic Formula

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

$$2a^{2}=16.97^{2}$$

Calculate 16.97 to the power of 2 and get 287.9809.

$$2a^{2}=287.9809$$

Subtract 287.9809 from both sides.

$$2a^{2}-287.9809=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -287.9809 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-287.9809\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-287.9809\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-287.9809\right)}}{2\times 2}$$

Multiply -8 times -287.9809.

$$a=\frac{0±\sqrt{2303.8472}}{2\times 2}$$

Take the square root of 2303.8472.

$$a=\frac{0±\frac{1697\sqrt{2}}{50}}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±\frac{1697\sqrt{2}}{50}}{4}$$

Now solve the equation a=\frac{0±\frac{1697\sqrt{2}}{50}}{4} when ± is plus.

$$a=\frac{1697\sqrt{2}}{200}$$

Now solve the equation a=\frac{0±\frac{1697\sqrt{2}}{50}}{4} when ± is minus.

$$a=-\frac{1697\sqrt{2}}{200}$$

The equation is now solved.

$$a=\frac{1697\sqrt{2}}{200} a=-\frac{1697\sqrt{2}}{200}$$