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Solve for $k$ . $\newline$ $k^2 + 4k + 4 = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $k =$ ____

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

k

.

\newline

k^2 + 4k + 4 = 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

k =

____

Identify Equation: Identify the quadratic equation to be solved. $\newline$ The given equation is $k^2 + 4k + 4 = 0$ . We need to find the values of $k$ that satisfy this equation.
Factor Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to give the constant term $4$ and add up to give the coefficient of the linear term $4$ . The numbers $2$ and $2$ satisfy these conditions because $2 \times 2 = 4$ and $2 + 2 = 4$ . $\newline$ So, we can write the equation as $(k + 2)(k + 2) = 0$ .
Set Equal Solve: Set each factor equal to zero and solve for $k$ . Since $(k + 2)(k + 2) = 0$ , we have two identical factors. We only need to set one of them equal to zero and solve for $k$ . $k + 2 = 0$ Subtract $2$ from both sides to solve for $k$ . $k = -2$
Write Solution: Write the solution to the equation. $\newline$ Since both factors are the same, we only have one unique solution for $k$ . $\newline$ The solution is $k = -2$ .

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