Solve for $v$ . $v^2+8v+12= 0$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $v= \,\_\_\_\_\_$

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Algebra 1

Solve a quadratic equation by factoring

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Q. Solve for

v

v^2+8v+12= 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= \,\_\_\_\_\_

Identify the quadratic equation: Identify the quadratic equation to be solved. $\newline$ We are given the quadratic equation $v^2 + 8v + 12 = 0$ . We need to find the values of $v$ that satisfy this equation.
Factor the quadratic equation: Factor the quadratic equation. $\newline$ To factor the equation, we need to find two numbers that multiply to give the constant term $12$ and add up to give the coefficient of the middle term $8$ . The numbers that satisfy these conditions are $2$ and $6$ , since $2 \times 6 = 12$ and $2 + 6 = 8$ .
Write the equation in factored form: Write the equation in factored form. $\newline$ Using the numbers found in Step $2$ , we can write the equation as $(v + 2)(v + 6) = 0$ .
Solve for $v$ using the zero product property: Solve for $v$ using the zero product property. $\newline$ The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for $v$ : $\newline$ $v + 2 = 0$ and $v + 6 = 0$ .
Solve the first equation: Solve the first equation $v + 2 = 0$ . $\newline$ Subtract $2$ from both sides to isolate $v$ : $\newline$ $v + 2 - 2 = 0 - 2$ $\newline$ $v = -2$
Solve the second equation: Solve the second equation $v + 6 = 0$ . $\newline$ Subtract $6$ from both sides to isolate $v$ : $\newline$ $v + 6 - 6 = 0 - 6$ $\newline$ $v = -6$