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Solve using the quadratic formula.\newlinez2+8z+8=0z^2 + 8z + 8 = 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.\newlinez2+8z+8=0z^2 + 8z + 8 = 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 of the quadratic equation az2+bz+c=0az^2 + bz + c = 0. In this case, a=1a = 1, b=8b = 8, and c=8c = 8.
  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 82−4(1)(8)=64−32=328^2 - 4(1)(8) = 64 - 32 = 32.
  3. Apply Quadratic Formula: Now, apply the quadratic formula with the calculated discriminant:\newlinez=−8±322×1z = \frac{-8 \pm \sqrt{32}}{2 \times 1}\newlinez=−8±16×22z = \frac{-8 \pm \sqrt{16 \times 2}}{2}\newlinez=−8±422z = \frac{-8 \pm 4\sqrt{2}}{2}
  4. Simplify Expression: Simplify the expression by dividing both terms in the numerator by 22:z=(−4±22)z = \left(-4 \pm 2\sqrt{2}\right)
  5. Find Solutions: We now have two solutions for zz:z=−4+22z = -4 + 2\sqrt{2} or z=−4−22z = -4 - 2\sqrt{2}These can be approximated as decimals if needed, but the question asks for integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
  6. Express as Decimals: To express the solutions as decimals rounded to the nearest hundredth, we calculate:\newlinez≈−4+2(1.41)≈−4+2.82≈−1.18z \approx -4 + 2(1.41) \approx -4 + 2.82 \approx -1.18\newlinez≈−4−2(1.41)≈−4−2.82≈−6.82z \approx -4 - 2(1.41) \approx -4 - 2.82 \approx -6.82

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