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Solve using the quadratic formula.\newline4h2+8h+4=04h^2 + 8h + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____

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Q. Solve using the quadratic formula.\newline4h2+8h+4=04h^2 + 8h + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____
  1. Identify coefficients: Identify the values of aa, bb, and cc in the quadratic equation 4h2+8h+4=04h^2 + 8h + 4 = 0.\newlineThe quadratic equation is in the form ah2+bh+c=0ah^2 + bh + c = 0, so by comparison:\newlinea=4a = 4\newlineb=8b = 8\newlinec=4c = 4
  2. Substitute into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find hh. The quadratic formula is h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get: h=−(8)±(8)2−4⋅4⋅42⋅4h = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot4\cdot4}}{2\cdot4}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (8)2−4⋅4⋅4=64−64=0\sqrt{(8)^2 - 4\cdot 4\cdot 4} = \sqrt{64 - 64} = \sqrt{0}
  4. Find real solution: Since the discriminant is 00, there is only one real solution.h=−8±08h = \frac{-8 \pm \sqrt{0}}{8}h=−8±08h = \frac{-8 \pm 0}{8}h=−88h = \frac{-8}{8}
  5. Simplify final answer: Simplify the fraction to find the value of hh.h=−88h = \frac{-8}{8}h=−1h = -1

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