Solve v_1^2=4*(2^circ41)^2

$$v _ { 1 } ^ { 2 } = 4 \times ( 2 ^ { \circ } 41 ) ^ { 2 }$$

Solve for v_1

$$v_{1}=164$$

$$v_{1}=-164$$

Steps Using Difference of Squares

Multiply 2 and 41 to get 82.

$$v_{1}^{2}=4\times 82^{2}$$

Calculate 82 to the power of 2 and get 6724.

$$v_{1}^{2}=4\times 6724$$

Multiply 4 and 6724 to get 26896.

$$v_{1}^{2}=26896$$

Subtract 26896 from both sides.

$$v_{1}^{2}-26896=0$$

Consider v_{1}^{2}-26896. Rewrite v_{1}^{2}-26896 as v_{1}^{2}-164^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v_{1}-164\right)\left(v_{1}+164\right)=0$$

To find equation solutions, solve v_{1}-164=0 and v_{1}+164=0.

$$v_{1}=164 v_{1}=-164$$

Steps by Finding Square Root

Multiply 2 and 41 to get 82.

$$v_{1}^{2}=4\times 82^{2}$$

Calculate 82 to the power of 2 and get 6724.

$$v_{1}^{2}=4\times 6724$$

Multiply 4 and 6724 to get 26896.

$$v_{1}^{2}=26896$$

Take the square root of both sides of the equation.

$$v_{1}=164 v_{1}=-164$$

Steps Using the Quadratic Formula

Multiply 2 and 41 to get 82.

$$v_{1}^{2}=4\times 82^{2}$$

Calculate 82 to the power of 2 and get 6724.

$$v_{1}^{2}=4\times 6724$$

Multiply 4 and 6724 to get 26896.

$$v_{1}^{2}=26896$$

Subtract 26896 from both sides.

$$v_{1}^{2}-26896=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -26896 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v_{1}=\frac{0±\sqrt{0^{2}-4\left(-26896\right)}}{2}$$

Square 0.

$$v_{1}=\frac{0±\sqrt{-4\left(-26896\right)}}{2}$$

Multiply -4 times -26896.

$$v_{1}=\frac{0±\sqrt{107584}}{2}$$

Take the square root of 107584.

$$v_{1}=\frac{0±328}{2}$$

Now solve the equation v_{1}=\frac{0±328}{2} when ± is plus. Divide 328 by 2.

$$v_{1}=164$$

Now solve the equation v_{1}=\frac{0±328}{2} when ± is minus. Divide -328 by 2.

$$v_{1}=-164$$

The equation is now solved.

$$v_{1}=164 v_{1}=-164$$