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Use the quadratic formula to solve. Express your answer in simplest form.
a^(2)+4a+4=0
a=◻

Use the quadratic formula to solve. Express your answer in simplest form. $\newline$ $a^{2}+4 a+4=0$ $\newline$ $a=\square$

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Conjugate root theorems

Full solution

Q. Use the quadratic formula to solve. Express your answer in simplest form.

\newline

a^{2}+4 a+4=0

\newline

a=\square

Quadratic Formula Explanation: The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $ax^2 + bx + c = 0$ . We will use this formula to find the roots of the given quadratic equation $a^2 + 4a + 4 = 0$ .
Identify Coefficients: First, identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation. In this case, $a = 1$ , $b = 4$ , and $c = 4$ .
Calculate Discriminant: Next, calculate the discriminant, which is $b^2 - 4ac$ . For our equation, the discriminant is $4^2 - 4(1)(4) = 16 - 16 = 0$ .
Apply Quadratic Formula: Since the discriminant is $0$ , there is only one real root, which is also called a repeated root. We can now apply the quadratic formula with the discriminant.
Substitute and Simplify: Substitute $a$ , $b$ , and $c$ into the quadratic formula: $a = \frac{-4 \pm \sqrt{0}}{2\times1} = \frac{-4 \pm 0}{2}$ .
Final Answer: Simplify the expression: $a = (-4) / 2 = -2$ .
Final Answer: Simplify the expression: $a = (-4) / 2 = -2$ .The final answer is that the quadratic equation $a^2 + 4a + 4 = 0$ has one repeated root, which is $a = -2$ .

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