Questions: Solve for (v). [ v^2+8 v+16=0 ] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution." [ v= ]

Solution Steps

To solve the quadratic equation \( v^2 + 8v + 16 = 0 \), we can use the quadratic formula \( v = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 8 \), and \( c = 16 \). This will give us the roots of the equation.

We start with the quadratic equation given by

\[ v^{2} + 8v + 16 = 0. \]

The discriminant \( D \) is calculated using the formula

\[ D = b^{2} - 4ac, \]

where \( a = 1 \), \( b = 8 \), and \( c = 16 \). Substituting the values, we find:

\[ D = 8^{2} - 4 \cdot 1 \cdot 16 = 64 - 64 = 0. \]

Since the discriminant \( D = 0 \), there is exactly one real solution (a repeated root). We can find the root using the formula

\[ v = \frac{-b \pm \sqrt{D}}{2a}. \]

Substituting the values, we have:

\[ v = \frac{-8 \pm \sqrt{0}}{2 \cdot 1} = \frac{-8}{2} = -4. \]

Final Answer