Question

solve for v.
$v^2 = 13v$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
v =
(there are some input buttons on the right side like fraction, mixed number, no solution, list of numbers, square root, and undo/delete buttons)

Explanation:

Step1: Move all terms to left

To solve the equation \(v^{2}=13v\), we first move all terms to one side of the equation. Subtract \(13v\) from both sides:
\(v^{2}-13v = 0\)

Step2: Factor the left - hand side

We can factor out the common factor \(v\) from the left - hand side of the equation \(v^{2}-13v = 0\). Using the distributive property \(ab+ac=a(b + c)\) (in reverse, where \(a = v\), \(b=v\) and \(c=- 13\)), we get:
\(v(v - 13)=0\)

Step3: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). So, for the equation \(v(v - 13)=0\), we have two cases:
Case 1: \(v=0\)
Case 2: \(v - 13=0\), which implies \(v=13\) when we add 13 to both sides of the equation.

Answer:

\(0,13\)