Solve 0.55*(L^2*35*100/0.5)=400

$$0.55 \times ( \frac { L ^ { 2 } \times 35 \times 100 } { 0.5 } ) = 400$$

Solve for L

$$L=\frac{2\sqrt{154}}{77}\approx 0.322329186$$

$$L=-\frac{2\sqrt{154}}{77}\approx -0.322329186$$

Steps by Finding Square Root

Divide both sides by 0.55.

$$\frac{L^{2}\times 35\times 100}{0.5}=\frac{400}{0.55}$$

Expand \frac{400}{0.55} by multiplying both numerator and the denominator by 100.

$$\frac{L^{2}\times 35\times 100}{0.5}=\frac{40000}{55}$$

Reduce the fraction \frac{40000}{55} to lowest terms by extracting and canceling out 5.

$$\frac{L^{2}\times 35\times 100}{0.5}=\frac{8000}{11}$$

Multiply both sides by 0.5.

$$L^{2}\times 35\times 100=\frac{8000}{11}\times 0.5$$

Multiply 35 and 100 to get 3500.

$$L^{2}\times 3500=\frac{8000}{11}\times 0.5$$

Multiply \frac{8000}{11} and 0.5 to get \frac{4000}{11}.

$$L^{2}\times 3500=\frac{4000}{11}$$

Divide both sides by 3500.

$$L^{2}=\frac{\frac{4000}{11}}{3500}$$

Express \frac{\frac{4000}{11}}{3500} as a single fraction.

$$L^{2}=\frac{4000}{11\times 3500}$$

Multiply 11 and 3500 to get 38500.

$$L^{2}=\frac{4000}{38500}$$

Reduce the fraction \frac{4000}{38500} to lowest terms by extracting and canceling out 500.

$$L^{2}=\frac{8}{77}$$

Take the square root of both sides of the equation.

$$L=\frac{2\sqrt{154}}{77} L=-\frac{2\sqrt{154}}{77}$$

Steps Using the Quadratic Formula

Divide both sides by 0.55.

$$\frac{L^{2}\times 35\times 100}{0.5}=\frac{400}{0.55}$$

Expand \frac{400}{0.55} by multiplying both numerator and the denominator by 100.

$$\frac{L^{2}\times 35\times 100}{0.5}=\frac{40000}{55}$$

Reduce the fraction \frac{40000}{55} to lowest terms by extracting and canceling out 5.

$$\frac{L^{2}\times 35\times 100}{0.5}=\frac{8000}{11}$$

Multiply both sides by 0.5.

$$L^{2}\times 35\times 100=\frac{8000}{11}\times 0.5$$

Multiply 35 and 100 to get 3500.

$$L^{2}\times 3500=\frac{8000}{11}\times 0.5$$

Multiply \frac{8000}{11} and 0.5 to get \frac{4000}{11}.

$$L^{2}\times 3500=\frac{4000}{11}$$

Subtract \frac{4000}{11} from both sides.

$$L^{2}\times 3500-\frac{4000}{11}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3500L^{2}-\frac{4000}{11}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3500 for a, 0 for b, and -\frac{4000}{11} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$L=\frac{0±\sqrt{0^{2}-4\times 3500\left(-\frac{4000}{11}\right)}}{2\times 3500}$$

Square 0.

$$L=\frac{0±\sqrt{-4\times 3500\left(-\frac{4000}{11}\right)}}{2\times 3500}$$

Multiply -4 times 3500.

$$L=\frac{0±\sqrt{-14000\left(-\frac{4000}{11}\right)}}{2\times 3500}$$

Multiply -14000 times -\frac{4000}{11}.

$$L=\frac{0±\sqrt{\frac{56000000}{11}}}{2\times 3500}$$

Take the square root of \frac{56000000}{11}.

$$L=\frac{0±\frac{2000\sqrt{154}}{11}}{2\times 3500}$$

Multiply 2 times 3500.

$$L=\frac{0±\frac{2000\sqrt{154}}{11}}{7000}$$

Now solve the equation L=\frac{0±\frac{2000\sqrt{154}}{11}}{7000} when ± is plus.

$$L=\frac{2\sqrt{154}}{77}$$

Now solve the equation L=\frac{0±\frac{2000\sqrt{154}}{11}}{7000} when ± is minus.

$$L=-\frac{2\sqrt{154}}{77}$$

The equation is now solved.

$$L=\frac{2\sqrt{154}}{77} L=-\frac{2\sqrt{154}}{77}$$