Answer:
The given equation has two solutions
[tex]v = (-5.29, \: 5.29)[/tex]
Step-by-step explanation:
The given equation is
[tex]3v^2 - 84 = 0[/tex]
Let’s solve the equation
[tex]3v^2 - 84 = 0 \\\\3v^2 = 84 \\\\v^2 = \frac{84}{3} \\\\v^2 = 28 \\\\[/tex]
Take the square root on both sides
[tex]\sqrt{v^2} = \sqrt{28} \\\\v = \sqrt{28} \\\\v = \pm 5.29 \\\\[/tex]
So the equation has two solutions
[tex]v = (-5.29, \: 5.29)[/tex]
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
[tex]\sqrt{25} = \pm 5 \\\\Since \\\\5 \times 5 = 25 \\\\-5 \times -5 = 25 \\\\[/tex]
That is why we have two solutions for the given equation.
