Solve 4v_1^2-0.8v_1^2=2.354

$$4 v _ { 1 } ^ { 2 } - 0.8 v _ { 1 } ^ { 2 } = 2.354$$

Solve for v_1

$$v_{1}=\frac{\sqrt{1177}}{40}\approx 0.85768584$$

$$v_{1}=-\frac{\sqrt{1177}}{40}\approx -0.85768584$$

Steps by Finding Square Root

Combine 4v_{1}^{2} and -0.8v_{1}^{2} to get 3.2v_{1}^{2}.

$$3.2v_{1}^{2}=2.354$$

Divide both sides by 3.2.

$$v_{1}^{2}=\frac{2.354}{3.2}$$

Expand \frac{2.354}{3.2} by multiplying both numerator and the denominator by 1000.

$$v_{1}^{2}=\frac{2354}{3200}$$

Reduce the fraction \frac{2354}{3200} to lowest terms by extracting and canceling out 2.

$$v_{1}^{2}=\frac{1177}{1600}$$

Take the square root of both sides of the equation.

$$v_{1}=\frac{\sqrt{1177}}{40} v_{1}=-\frac{\sqrt{1177}}{40}$$

Steps Using the Quadratic Formula

Combine 4v_{1}^{2} and -0.8v_{1}^{2} to get 3.2v_{1}^{2}.

$$3.2v_{1}^{2}=2.354$$

Subtract 2.354 from both sides.

$$3.2v_{1}^{2}-2.354=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3.2 for a, 0 for b, and -2.354 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v_{1}=\frac{0±\sqrt{0^{2}-4\times 3.2\left(-2.354\right)}}{2\times 3.2}$$

Square 0.

$$v_{1}=\frac{0±\sqrt{-4\times 3.2\left(-2.354\right)}}{2\times 3.2}$$

Multiply -4 times 3.2.

$$v_{1}=\frac{0±\sqrt{-12.8\left(-2.354\right)}}{2\times 3.2}$$

Multiply -12.8 times -2.354 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$v_{1}=\frac{0±\sqrt{30.1312}}{2\times 3.2}$$

Take the square root of 30.1312.

$$v_{1}=\frac{0±\frac{4\sqrt{1177}}{25}}{2\times 3.2}$$

Multiply 2 times 3.2.

$$v_{1}=\frac{0±\frac{4\sqrt{1177}}{25}}{6.4}$$

Now solve the equation v_{1}=\frac{0±\frac{4\sqrt{1177}}{25}}{6.4} when ± is plus.

$$v_{1}=\frac{\sqrt{1177}}{40}$$

Now solve the equation v_{1}=\frac{0±\frac{4\sqrt{1177}}{25}}{6.4} when ± is minus.

$$v_{1}=-\frac{\sqrt{1177}}{40}$$

The equation is now solved.

$$v_{1}=\frac{\sqrt{1177}}{40} v_{1}=-\frac{\sqrt{1177}}{40}$$