Solve a^2+a^2=29.698^2

$$a ^ { 2 } + a ^ { 2 } = 29.698 ^ { 2 }$$

Solve for a

$$a = \frac{14849 \sqrt{2}}{1000} \approx 20.999657188$$

$$a = -\frac{14849 \sqrt{2}}{1000} \approx -20.999657188$$

Steps by Finding Square Root

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

$$2a^{2}=29.698^{2}$$

Calculate 29.698 to the power of 2 and get 881.971204.

$$2a^{2}=881.971204$$

Divide both sides by 2.

$$a^{2}=\frac{881.971204}{2}$$

Expand \frac{881.971204}{2} by multiplying both numerator and the denominator by 1000000.

$$a^{2}=\frac{881971204}{2000000}$$

Reduce the fraction \frac{881971204}{2000000} to lowest terms by extracting and canceling out 4.

$$a^{2}=\frac{220492801}{500000}$$

Take the square root of both sides of the equation.

$$a=\frac{14849\sqrt{2}}{1000} a=-\frac{14849\sqrt{2}}{1000}$$

Steps Using the Quadratic Formula

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

$$2a^{2}=29.698^{2}$$

Calculate 29.698 to the power of 2 and get 881.971204.

$$2a^{2}=881.971204$$

Subtract 881.971204 from both sides.

$$2a^{2}-881.971204=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -881.971204 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-881.971204\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-881.971204\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-881.971204\right)}}{2\times 2}$$

Multiply -8 times -881.971204.

$$a=\frac{0±\sqrt{7055.769632}}{2\times 2}$$

Take the square root of 7055.769632.

$$a=\frac{0±\frac{14849\sqrt{2}}{250}}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±\frac{14849\sqrt{2}}{250}}{4}$$

Now solve the equation a=\frac{0±\frac{14849\sqrt{2}}{250}}{4} when ± is plus.

$$a=\frac{14849\sqrt{2}}{1000}$$

Now solve the equation a=\frac{0±\frac{14849\sqrt{2}}{250}}{4} when ± is minus.

$$a=-\frac{14849\sqrt{2}}{1000}$$

The equation is now solved.

$$a=\frac{14849\sqrt{2}}{1000} a=-\frac{14849\sqrt{2}}{1000}$$