Solve 592y^2=106856*10^18-5*624*10^99

$$592 y ^ { 2 } = 106856 \times 10 ^ { 18 } - 5 \cdot 624 \times 10 ^ { 9 } 9$$

Solve for y

$$y = \frac{50000 \sqrt{98841799974026}}{37} \approx 13435028840.779150009$$

$$y = -\frac{50000 \sqrt{98841799974026}}{37} \approx -13435028840.779150009$$

Steps by Finding Square Root

Calculate 10 to the power of 18 and get 1000000000000000000.

$$592y^{2}=106856\times 1000000000000000000-5\times 624\times 10^{9}\times 9$$

Multiply 106856 and 1000000000000000000 to get 106856000000000000000000.

$$592y^{2}=106856000000000000000000-5\times 624\times 10^{9}\times 9$$

Multiply 5 and 624 to get 3120.

$$592y^{2}=106856000000000000000000-3120\times 10^{9}\times 9$$

Calculate 10 to the power of 9 and get 1000000000.

$$592y^{2}=106856000000000000000000-3120\times 1000000000\times 9$$

Multiply 3120 and 1000000000 to get 3120000000000.

$$592y^{2}=106856000000000000000000-3120000000000\times 9$$

Multiply 3120000000000 and 9 to get 28080000000000.

$$592y^{2}=106856000000000000000000-28080000000000$$

Subtract 28080000000000 from 106856000000000000000000 to get 106855999971920000000000.

$$592y^{2}=106855999971920000000000$$

Divide both sides by 592.

$$y^{2}=\frac{106855999971920000000000}{592}$$

Reduce the fraction \frac{106855999971920000000000}{592} to lowest terms by extracting and canceling out 16.

$$y^{2}=\frac{6678499998245000000000}{37}$$

Take the square root of both sides of the equation.

$$y=\frac{50000\sqrt{98841799974026}}{37} y=-\frac{50000\sqrt{98841799974026}}{37}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 18 and get 1000000000000000000.

$$592y^{2}=106856\times 1000000000000000000-5\times 624\times 10^{9}\times 9$$

Multiply 106856 and 1000000000000000000 to get 106856000000000000000000.

$$592y^{2}=106856000000000000000000-5\times 624\times 10^{9}\times 9$$

Multiply 5 and 624 to get 3120.

$$592y^{2}=106856000000000000000000-3120\times 10^{9}\times 9$$

Calculate 10 to the power of 9 and get 1000000000.

$$592y^{2}=106856000000000000000000-3120\times 1000000000\times 9$$

Multiply 3120 and 1000000000 to get 3120000000000.

$$592y^{2}=106856000000000000000000-3120000000000\times 9$$

Multiply 3120000000000 and 9 to get 28080000000000.

$$592y^{2}=106856000000000000000000-28080000000000$$

Subtract 28080000000000 from 106856000000000000000000 to get 106855999971920000000000.

$$592y^{2}=106855999971920000000000$$

Subtract 106855999971920000000000 from both sides.

$$592y^{2}-106855999971920000000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 592 for a, 0 for b, and -106855999971920000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 592\left(-106855999971920000000000\right)}}{2\times 592}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 592\left(-106855999971920000000000\right)}}{2\times 592}$$

Multiply -4 times 592.

$$y=\frac{0±\sqrt{-2368\left(-106855999971920000000000\right)}}{2\times 592}$$

Multiply -2368 times -106855999971920000000000.

$$y=\frac{0±\sqrt{253035007933506560000000000}}{2\times 592}$$

Take the square root of 253035007933506560000000000.

$$y=\frac{0±1600000\sqrt{98841799974026}}{2\times 592}$$

Multiply 2 times 592.

$$y=\frac{0±1600000\sqrt{98841799974026}}{1184}$$

Now solve the equation y=\frac{0±1600000\sqrt{98841799974026}}{1184} when ± is plus.

$$y=\frac{50000\sqrt{98841799974026}}{37}$$

Now solve the equation y=\frac{0±1600000\sqrt{98841799974026}}{1184} when ± is minus.

$$y=-\frac{50000\sqrt{98841799974026}}{37}$$

The equation is now solved.

$$y=\frac{50000\sqrt{98841799974026}}{37} y=-\frac{50000\sqrt{98841799974026}}{37}$$