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

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

Solve for L

$$L=\frac{\sqrt{70}}{35}\approx 0.239045722$$

$$L=-\frac{\sqrt{70}}{35}\approx -0.239045722$$

Steps by Finding Square Root

Multiply both sides by 0.5.

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

Multiply 35 and 100 to get 3500.

$$L^{2}\times 3500=400\times 0.5$$

Multiply 400 and 0.5 to get 200.

$$L^{2}\times 3500=200$$

Divide both sides by 3500.

$$L^{2}=\frac{200}{3500}$$

Reduce the fraction \frac{200}{3500} to lowest terms by extracting and canceling out 100.

$$L^{2}=\frac{2}{35}$$

Take the square root of both sides of the equation.

$$L=\frac{\sqrt{70}}{35} L=-\frac{\sqrt{70}}{35}$$

Steps Using the Quadratic Formula

Multiply both sides by 0.5.

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

Multiply 35 and 100 to get 3500.

$$L^{2}\times 3500=400\times 0.5$$

Multiply 400 and 0.5 to get 200.

$$L^{2}\times 3500=200$$

Subtract 200 from both sides.

$$L^{2}\times 3500-200=0$$

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.

$$3500L^{2}-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3500 for a, 0 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$L=\frac{0±\sqrt{0^{2}-4\times 3500\left(-200\right)}}{2\times 3500}$$

Square 0.

$$L=\frac{0±\sqrt{-4\times 3500\left(-200\right)}}{2\times 3500}$$

Multiply -4 times 3500.

$$L=\frac{0±\sqrt{-14000\left(-200\right)}}{2\times 3500}$$

Multiply -14000 times -200.

$$L=\frac{0±\sqrt{2800000}}{2\times 3500}$$

Take the square root of 2800000.

$$L=\frac{0±200\sqrt{70}}{2\times 3500}$$

Multiply 2 times 3500.

$$L=\frac{0±200\sqrt{70}}{7000}$$

Now solve the equation L=\frac{0±200\sqrt{70}}{7000} when ± is plus.

$$L=\frac{\sqrt{70}}{35}$$

Now solve the equation L=\frac{0±200\sqrt{70}}{7000} when ± is minus.

$$L=-\frac{\sqrt{70}}{35}$$

The equation is now solved.

$$L=\frac{\sqrt{70}}{35} L=-\frac{\sqrt{70}}{35}$$