Solve 592*6y^2=1.06856*10^18-5.624*10^9

$$592 \cdot 6 y ^ { 2 } = 1.06856 \times 10 ^ { 18 } - 5.624 \times 10 ^ { 9 }$$

Solve for y

$$y=283500\sqrt{3743}\approx 17344547.608686715$$

$$y=-283500\sqrt{3743}\approx -17344547.608686715$$

Steps by Finding Square Root

Multiply 592 and 6 to get 3552.

$$3552y^{2}=1.06856\times 10^{18}-5.624\times 10^{9}$$

Calculate 10 to the power of 18 and get 1000000000000000000.

$$3552y^{2}=1.06856\times 1000000000000000000-5.624\times 10^{9}$$

Multiply 1.06856 and 1000000000000000000 to get 1068560000000000000.

$$3552y^{2}=1068560000000000000-5.624\times 10^{9}$$

Calculate 10 to the power of 9 and get 1000000000.

$$3552y^{2}=1068560000000000000-5.624\times 1000000000$$

Multiply 5.624 and 1000000000 to get 5624000000.

$$3552y^{2}=1068560000000000000-5624000000$$

Subtract 5624000000 from 1068560000000000000 to get 1068559994376000000.

$$3552y^{2}=1068559994376000000$$

Divide both sides by 3552.

$$y^{2}=\frac{1068559994376000000}{3552}$$

Divide 1068559994376000000 by 3552 to get 300833331750000.

$$y^{2}=300833331750000$$

Take the square root of both sides of the equation.

$$y=283500\sqrt{3743} y=-283500\sqrt{3743}$$

Steps Using the Quadratic Formula

Multiply 592 and 6 to get 3552.

$$3552y^{2}=1.06856\times 10^{18}-5.624\times 10^{9}$$

Calculate 10 to the power of 18 and get 1000000000000000000.

$$3552y^{2}=1.06856\times 1000000000000000000-5.624\times 10^{9}$$

Multiply 1.06856 and 1000000000000000000 to get 1068560000000000000.

$$3552y^{2}=1068560000000000000-5.624\times 10^{9}$$

Calculate 10 to the power of 9 and get 1000000000.

$$3552y^{2}=1068560000000000000-5.624\times 1000000000$$

Multiply 5.624 and 1000000000 to get 5624000000.

$$3552y^{2}=1068560000000000000-5624000000$$

Subtract 5624000000 from 1068560000000000000 to get 1068559994376000000.

$$3552y^{2}=1068559994376000000$$

Subtract 1068559994376000000 from both sides.

$$3552y^{2}-1068559994376000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3552 for a, 0 for b, and -1068559994376000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 3552\left(-1068559994376000000\right)}}{2\times 3552}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 3552\left(-1068559994376000000\right)}}{2\times 3552}$$

Multiply -4 times 3552.

$$y=\frac{0±\sqrt{-14208\left(-1068559994376000000\right)}}{2\times 3552}$$

Multiply -14208 times -1068559994376000000.

$$y=\frac{0±\sqrt{15182100400094208000000}}{2\times 3552}$$

Take the square root of 15182100400094208000000.

$$y=\frac{0±2013984000\sqrt{3743}}{2\times 3552}$$

Multiply 2 times 3552.

$$y=\frac{0±2013984000\sqrt{3743}}{7104}$$

Now solve the equation y=\frac{0±2013984000\sqrt{3743}}{7104} when ± is plus.

$$y=283500\sqrt{3743}$$

Now solve the equation y=\frac{0±2013984000\sqrt{3743}}{7104} when ± is minus.

$$y=-283500\sqrt{3743}$$

The equation is now solved.

$$y=283500\sqrt{3743} y=-283500\sqrt{3743}$$