Question

solve for v.
$v^2 + 20v + 100 = 0$
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
$v = $

Explanation:

Step1: Recognize the quadratic form

The equation \(v^2 + 20v + 100 = 0\) is a quadratic equation. We can try to factor it. Notice that it is a perfect square trinomial. The form of a perfect square trinomial is \(a^2 + 2ab + b^2=(a + b)^2\). Here, \(a = v\), \(2ab=20v\) (so \(b = 10\) since \(2\times v\times10=20v\)) and \(b^2 = 100\). So we can factor the left - hand side as \((v + 10)^2=0\).

Step2: Solve for v

To solve \((v + 10)^2=0\), we take the square root of both sides. The square root of a number squared is the absolute value of the number, but since the right - hand side is 0, we have \(v+10 = 0\) (because \(\sqrt{0}=0\)). Then, we solve for \(v\) by subtracting 10 from both sides of the equation: \(v=- 10\).

Answer:

\(-10\)