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Solve for $v$ . $\newline$ $v^2 + 8v + 7 = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $v =$ ____

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

v

.

\newline

v^2 + 8v + 7 = 0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

v =

____

Identify Equation: Identify the quadratic equation to be solved. $\newline$ We have the quadratic equation $v^2 + 8v + 7 = 0$ .
Factor Equation: Factor the quadratic equation, if possible. $\newline$ We need to find two numbers that multiply to $7$ (the constant term) and add up to $8$ (the coefficient of the $v$ term). The numbers $1$ and $7$ fit this requirement because $1 \times 7 = 7$ and $1 + 7 = 8$ .
Write Factored Form: Write the factored form of the equation. $\newline$ The equation can be factored as $(v + 1)(v + 7) = 0$ .
Solve for $v$ : Set each factor equal to zero and solve for $v$ . $\newline$ First, set $v + 1 = 0$ and solve for $v$ . $\newline$ $v + 1 - 1 = 0 - 1$ $\newline$ $v = -1$
Solve Second Factor: Solve the second factor. $\newline$ Now, set $v + 7 = 0$ and solve for $v$ . $\newline$ $v + 7 - 7 = 0 - 7$ $\newline$ $v = -7$
Write Solutions: Write the solutions of the equation $v^2 + 8v + 7 = 0$ . The values of $v$ are $-1$ and $-7$ .

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