Solve (8314*273)^2*(a^2-01a)=231*10^6

$$( 8314 \times 273 ) ^ { 2 } \times ( a ^ { 2 } - 01 a ) = 231 \times 10 ^ { 6 }$$

Solve for a

$$a=\frac{500\sqrt{231}}{1134861}\approx 0.006696276$$

$$a=-\frac{500\sqrt{231}}{1134861}\approx -0.006696276$$

Steps by Finding Square Root

Multiply 8314 and 273 to get 2269722.

$$2269722^{2}\left(a^{2}-0\times 1a\right)=231\times 10^{6}$$

Calculate 2269722 to the power of 2 and get 5151637957284.

$$5151637957284\left(a^{2}-0\times 1a\right)=231\times 10^{6}$$

Multiply 0 and 1 to get 0.

$$5151637957284\left(a^{2}-0a\right)=231\times 10^{6}$$

Anything times zero gives zero.

$$5151637957284\left(a^{2}-0\right)=231\times 10^{6}$$

Calculate 10 to the power of 6 and get 1000000.

$$5151637957284\left(a^{2}-0\right)=231\times 1000000$$

Multiply 231 and 1000000 to get 231000000.

$$5151637957284\left(a^{2}-0\right)=231000000$$

Divide both sides by 5151637957284.

$$a^{2}-0=\frac{231000000}{5151637957284}$$

Reduce the fraction \frac{231000000}{5151637957284} to lowest terms by extracting and canceling out 84.

$$a^{2}-0=\frac{2750000}{61329023301}$$

Reorder the terms.

$$a^{2}=\frac{2750000}{61329023301}$$

Take the square root of both sides of the equation.

$$a=\frac{500\sqrt{231}}{1134861} a=-\frac{500\sqrt{231}}{1134861}$$

Steps Using the Quadratic Formula

Multiply 8314 and 273 to get 2269722.

$$2269722^{2}\left(a^{2}-0\times 1a\right)=231\times 10^{6}$$

Calculate 2269722 to the power of 2 and get 5151637957284.

$$5151637957284\left(a^{2}-0\times 1a\right)=231\times 10^{6}$$

Multiply 0 and 1 to get 0.

$$5151637957284\left(a^{2}-0a\right)=231\times 10^{6}$$

Anything times zero gives zero.

$$5151637957284\left(a^{2}-0\right)=231\times 10^{6}$$

Calculate 10 to the power of 6 and get 1000000.

$$5151637957284\left(a^{2}-0\right)=231\times 1000000$$

Multiply 231 and 1000000 to get 231000000.

$$5151637957284\left(a^{2}-0\right)=231000000$$

Subtract 231000000 from both sides.

$$5151637957284\left(a^{2}-0\right)-231000000=0$$

Reorder the terms.

$$5151637957284a^{2}-231000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5151637957284 for a, 0 for b, and -231000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 5151637957284\left(-231000000\right)}}{2\times 5151637957284}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 5151637957284\left(-231000000\right)}}{2\times 5151637957284}$$

Multiply -4 times 5151637957284.

$$a=\frac{0±\sqrt{-20606551829136\left(-231000000\right)}}{2\times 5151637957284}$$

Multiply -20606551829136 times -231000000.

$$a=\frac{0±\sqrt{4760113472530416000000}}{2\times 5151637957284}$$

Take the square root of 4760113472530416000000.

$$a=\frac{0±4539444000\sqrt{231}}{2\times 5151637957284}$$

Multiply 2 times 5151637957284.

$$a=\frac{0±4539444000\sqrt{231}}{10303275914568}$$

Now solve the equation a=\frac{0±4539444000\sqrt{231}}{10303275914568} when ± is plus.

$$a=\frac{500\sqrt{231}}{1134861}$$

Now solve the equation a=\frac{0±4539444000\sqrt{231}}{10303275914568} when ± is minus.

$$a=-\frac{500\sqrt{231}}{1134861}$$

The equation is now solved.

$$a=\frac{500\sqrt{231}}{1134861} a=-\frac{500\sqrt{231}}{1134861}$$