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Solve using the quadratic formula. \newline 7m2−9m+2=07m^2 - 9m + 2 = 0 \newline Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. \newline m=m = □\square or m=m =□\square

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Q. Solve using the quadratic formula. \newline 7m2−9m+2=07m^2 - 9m + 2 = 0 \newline Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. \newline m=m = □\square or m=m =□\square
  1. Write Quadratic Formula: Write down the quadratic formula.\newlineThe quadratic formula is used to solve for the roots of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 and is given by x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  2. Identify Coefficients: Identify the coefficients aa, bb, and cc from the quadratic equation 7m2−9m+2=07m^2 − 9m + 2 = 0. Here, a=7a = 7, b=−9b = -9, and c=2c = 2.
  3. Substitute into Formula: Substitute the coefficients into the quadratic formula.\newlinem=−(−9)±(−9)2−4⋅7⋅22⋅7m = \frac{-(-9) \pm \sqrt{(-9)^2 - 4 \cdot 7 \cdot 2}}{2 \cdot 7}\newlinem=9±81−5614m = \frac{9 \pm \sqrt{81 - 56}}{14}
  4. Simplify Discriminant: Simplify the expression under the square root (the discriminant).\newlinem=9±2514m = \frac{9 \pm \sqrt{25}}{14}\newlinem=9±514m = \frac{9 \pm 5}{14}
  5. Solve for Values: Solve for the two possible values of mm.\newlineFirst solution:\newlinem=9+514m = \frac{9 + 5}{14}\newlinem=1414m = \frac{14}{14}\newlinem=1m = 1\newlineSecond solution:\newlinem=9−514m = \frac{9 - 5}{14}\newlinem=414m = \frac{4}{14}\newlinem=27m = \frac{2}{7} after simplifying the fraction.

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