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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.\newlinea2+4a+4=0 a^{2}+4 a+4=0 \newlinea= a=\square

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Q. Use the quadratic formula to solve. Express your answer in simplest form.\newlinea2+4a+4=0 a^{2}+4 a+4=0 \newlinea= a=\square
  1. Quadratic Formula Explanation: The quadratic formula is given by x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where ax2+bx+c=0ax^2 + bx + c = 0. We will use this formula to find the roots of the given quadratic equation a2+4a+4=0a^2 + 4a + 4 = 0.
  2. Identify Coefficients: First, identify the coefficients aa, bb, and cc from the quadratic equation. In this case, a=1a = 1, b=4b = 4, and c=4c = 4.
  3. Calculate Discriminant: Next, calculate the discriminant, which is b24acb^2 - 4ac. For our equation, the discriminant is 424(1)(4)=1616=04^2 - 4(1)(4) = 16 - 16 = 0.
  4. Apply Quadratic Formula: Since the discriminant is 00, there is only one real root, which is also called a repeated root. We can now apply the quadratic formula with the discriminant.
  5. Substitute and Simplify: Substitute aa, bb, and cc into the quadratic formula: a=4±02×1=4±02a = \frac{-4 \pm \sqrt{0}}{2\times1} = \frac{-4 \pm 0}{2}.
  6. Final Answer: Simplify the expression: a=(4)/2=2a = (-4) / 2 = -2.
  7. Final Answer: Simplify the expression: a=(4)/2=2a = (-4) / 2 = -2.The final answer is that the quadratic equation a2+4a+4=0a^2 + 4a + 4 = 0 has one repeated root, which is a=2a = -2.

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