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Solve using the quadratic formula.\newlinem2+5m+1=0m^2 + 5m + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____

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Q. Solve using the quadratic formula.\newlinem2+5m+1=0m^2 + 5m + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____
  1. Quadratic Formula: The quadratic formula is given by m=−b±b2−4ac2am = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation am2+bm+c=0am^2 + bm + c = 0. In this case, a=1a = 1, b=5b = 5, and c=1c = 1.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is 52−4(1)(1)=25−4=215^2 - 4(1)(1) = 25 - 4 = 21.
  3. Apply Quadratic Formula: Now, apply the quadratic formula with the values of aa, bb, and cc:m=−5±212×1m = \frac{{-5 \pm \sqrt{21}}}{{2 \times 1}}m=−5±212m = \frac{{-5 \pm \sqrt{21}}}{2}
  4. Calculate Real Solutions: Since the discriminant is positive, there will be two real solutions. We need to calculate both:\newlinem1=−5+212m_1 = \frac{-5 + \sqrt{21}}{2}\newlinem2=−5−212m_2 = \frac{-5 - \sqrt{21}}{2}
  5. Express Solutions as Decimals: The solutions cannot be simplified to integers or proper fractions. We can express them as decimals rounded to the nearest hundredth:\newlinem1≈(−5+4.58)/2≈−0.21m_1 \approx (-5 + 4.58) / 2 \approx -0.21\newlinem2≈(−5−4.58)/2≈−4.79m_2 \approx (-5 - 4.58) / 2 \approx -4.79

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