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Solve using the quadratic formula.\newlinew2+2w+1=0w^2 + 2w + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

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Q. Solve using the quadratic formula.\newlinew2+2w+1=0w^2 + 2w + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Quadratic Formula Explanation: The quadratic formula is used to solve equations of the form ax2+bx+c=0ax^2 + bx + c = 0. The formula is given by x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. For the equation w2+2w+1=0w^2 + 2w + 1 = 0, we have a=1a = 1, b=2b = 2, and c=1c = 1.
  2. Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, the discriminant is (2)2−4(1)(1)=4−4=0(2)^2 - 4(1)(1) = 4 - 4 = 0.
  3. Apply Quadratic Formula: Since the discriminant is 00, this means that there is only one real solution to the equation, because the square root of 00 is 00. We can proceed to apply the quadratic formula with the discriminant.
  4. Solve for w: Using the quadratic formula with our values of aa, bb, and cc, we get w=−2±02⋅1w = \frac{-2 \pm \sqrt{0}}{2\cdot1}. This simplifies to w=−2±02w = \frac{-2 \pm 0}{2}.
  5. Solve for w: Using the quadratic formula with our values of aa, bb, and cc, we get w=−2±02⋅1w = \frac{-2 \pm \sqrt{0}}{2\cdot1}. This simplifies to w=−2±02w = \frac{-2 \pm 0}{2}. Simplifying further, we find that w=−22w = \frac{-2}{2}, which gives us w=−1w = -1.

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