Solve (0.00378541)(27)(1.5)/(1.5)=k^2/2

$$\frac { ( 0.00378541 ) ( 27 ) ( 1.5 ) } { ( 1.5 ) } = \frac { k ^ { 2 } } { 2 }$$

Solve for k

$$k=\frac{3\sqrt{2271246}}{10000}\approx 0.452119608$$

$$k=-\frac{3\sqrt{2271246}}{10000}\approx -0.452119608$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$2\times \frac{0.00378541\times 27\times 1.5}{1.5}=k^{2}$$

Cancel out 1.5 and 1.5.

$$2\times 0.00378541\times 27=k^{2}$$

Multiply 0.00378541 and 27 to get 0.10220607.

$$2\times 0.10220607=k^{2}$$

Multiply 2 and 0.10220607 to get 0.20441214.

$$0.20441214=k^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$k^{2}=0.20441214$$

Take the square root of both sides of the equation.

$$k=\frac{3\sqrt{2271246}}{10000} k=-\frac{3\sqrt{2271246}}{10000}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$2\times \frac{0.00378541\times 27\times 1.5}{1.5}=k^{2}$$

Cancel out 1.5 and 1.5.

$$2\times 0.00378541\times 27=k^{2}$$

Multiply 0.00378541 and 27 to get 0.10220607.

$$2\times 0.10220607=k^{2}$$

Multiply 2 and 0.10220607 to get 0.20441214.

$$0.20441214=k^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$k^{2}=0.20441214$$

Subtract 0.20441214 from both sides.

$$k^{2}-0.20441214=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -0.20441214 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-0.20441214\right)}}{2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-0.20441214\right)}}{2}$$

Multiply -4 times -0.20441214.

$$k=\frac{0±\sqrt{0.81764856}}{2}$$

Take the square root of 0.81764856.

$$k=\frac{0±\frac{3\sqrt{2271246}}{5000}}{2}$$

Now solve the equation k=\frac{0±\frac{3\sqrt{2271246}}{5000}}{2} when ± is plus.

$$k=\frac{3\sqrt{2271246}}{10000}$$

Now solve the equation k=\frac{0±\frac{3\sqrt{2271246}}{5000}}{2} when ± is minus.

$$k=-\frac{3\sqrt{2271246}}{10000}$$

The equation is now solved.

$$k=\frac{3\sqrt{2271246}}{10000} k=-\frac{3\sqrt{2271246}}{10000}$$