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Solve using the quadratic formula.\newline2z2+9z+9=02z^2 + 9z + 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____

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Q. Solve using the quadratic formula.\newline2z2+9z+9=02z^2 + 9z + 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____
  1. Quadratic Formula: The quadratic formula is given by z=−b±b2−4ac2az = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation az2+bz+c=0az^2 + bz + c = 0. In this case, a=2a = 2, b=9b = 9, and c=9c = 9.
  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(2)(9)9^2 - 4(2)(9).
  3. Find Discriminant: Perform the calculation: 81−72=981 - 72 = 9.
  4. Plug into Formula: Now, plug the discriminant back into the quadratic formula to find the two possible values for zz. We have z=−9±92×2z = \frac{-9 \pm \sqrt{9}}{2 \times 2}.
  5. Simplify Square Root: Simplify the square root of the discriminant: 9=3\sqrt{9} = 3.
  6. Positive Square Root: Now, solve for the two possible values of zz. First, the positive square root: z=(−9+3)/4z = (-9 + 3) / 4.
  7. Negative Square Root: Perform the calculation: z=(−6)/4=−32z = (-6) / 4 = -\frac{3}{2} or −1.5-1.5.
  8. Final Calculation: Next, solve for zz using the negative square root: z=($−9z = (\$-9 −3- 3) / 44\).
  9. Final Calculation: Next, solve for zz using the negative square root: z=(−9−3)/4z = (-9 - 3) / 4.Perform the calculation: z=(−12)/4=−3z = (-12) / 4 = -3.

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