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Solve using the quadratic formula.\newline9m2+9m+2=09m^2 + 9m + 2 = 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.\newline9m2+9m+2=09m^2 + 9m + 2 = 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 Explanation: 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 of the terms in the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=9a = 9, b=9b = 9, and c=2c = 2.
  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 92−4(9)(2)9^2 - 4(9)(2).
  3. Discriminant Calculation: Perform the calculation: 81−72=981 - 72 = 9.
  4. Plug into Quadratic Formula: Now, plug the discriminant back into the quadratic formula to find the two possible values for mm. We have m=−9±92×9m = \frac{-9 \pm \sqrt{9}}{2 \times 9}.
  5. Simplify Square Root: Simplify the square root of the discriminant: 9=3\sqrt{9} = 3.
  6. Positive Square Root Calculation: Now, solve for the two possible values of mm. First, the positive square root: m=(−9+3)/18m = (-9 + 3) / 18.
  7. Positive Square Root Simplification: Perform the calculation: m=−618m = \frac{-6}{18}.
  8. Negative Square Root Calculation: Simplify the fraction: m=−13m = -\frac{1}{3}.
  9. Negative Square Root Simplification: Next, solve for mm using the negative square root: m=(−9−3)/18m = ( -9 - 3 ) / 18.
  10. Negative Square Root Simplification: Next, solve for mm using the negative square root: m=(−9−3)/18m = (-9 - 3) / 18.Perform the calculation: m=(−12)/18m = (-12) / 18.
  11. Negative Square Root Simplification: Next, solve for mm using the negative square root: m=(−9−3)/18m = (-9 - 3) / 18.Perform the calculation: m=(−12)/18m = (-12) / 18.Simplify the fraction: m=−2/3m = -2/3.

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