Solve 7v^2+1=29

$$7 v ^ { 2 } + 1 = 29$$

Solve for v

$$v=2$$

$$v=-2$$

Steps Using Difference of Squares

Subtract 29 from both sides.

$$7v^{2}+1-29=0$$

Subtract 29 from 1 to get -28.

$$7v^{2}-28=0$$

Divide both sides by 7.

$$v^{2}-4=0$$

Consider v^{2}-4. Rewrite v^{2}-4 as v^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-2\right)\left(v+2\right)=0$$

To find equation solutions, solve v-2=0 and v+2=0.

$$v=2 v=-2$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$7v^{2}=29-1$$

Subtract 1 from 29 to get 28.

$$7v^{2}=28$$

Divide both sides by 7.

$$v^{2}=\frac{28}{7}$$

Divide 28 by 7 to get 4.

$$v^{2}=4$$

Take the square root of both sides of the equation.

$$v=2 v=-2$$

Steps Using the Quadratic Formula

Subtract 29 from both sides.

$$7v^{2}+1-29=0$$

Subtract 29 from 1 to get -28.

$$7v^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times 7\left(-28\right)}}{2\times 7}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times 7\left(-28\right)}}{2\times 7}$$

Multiply -4 times 7.

$$v=\frac{0±\sqrt{-28\left(-28\right)}}{2\times 7}$$

Multiply -28 times -28.

$$v=\frac{0±\sqrt{784}}{2\times 7}$$

Take the square root of 784.

$$v=\frac{0±28}{2\times 7}$$

Multiply 2 times 7.

$$v=\frac{0±28}{14}$$

Now solve the equation v=\frac{0±28}{14} when ± is plus. Divide 28 by 14.

$$v=2$$

Now solve the equation v=\frac{0±28}{14} when ± is minus. Divide -28 by 14.

$$v=-2$$

The equation is now solved.

$$v=2 v=-2$$