Question

Solve 3v2 – 84 = 0, where v is a real number.

Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".

Answer 1

The given equation has two solutions

`v = (-5.29, \: 5.29)`

Step-by-step explanation:

The given equation is

`3v^2 - 84 = 0`

Let’s solve the equation

`3v^2 - 84 = 0 \\\\3v^2 = 84 \\\\v^2 = (84)/(3) \\\\v^2 = 28 \\\\`

Take the square root on both sides

`√(v^2) = √(28) \\\\v = √(28) \\\\v = \pm 5.29 \\\\`

So the equation has two solutions

`v = (-5.29, \: 5.29)`

Also refer to the attached graph of the equation where you can verify that the equation has two solutions.

Note:

It is a very common mistake to consider only the positive value and not the negative value.

Consider the square root of 25

`√(25) = \pm 5 \\\\Since \\\\5 * 5 = 25 \\\\-5 * -5 = 25 \\\\`

That is why we have two solutions for the given equation.