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Solve using the quadratic formula.\newlinez2+7z+4=0z^2 + 7z + 4 = 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+7z+4=0z^2 + 7z + 4 = 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. Write Quadratic Formula: Write down the quadratic formula.\newlineThe quadratic formula is used to solve equations of the form ax2+bx+c=0ax^2 + bx + c = 0. The formula is:\newlinez=−b±b2−4ac2az = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\newlineIn our equation, a=1a = 1, b=7b = 7, and c=4c = 4.
  2. Substitute Values: Substitute the values of aa, bb, and cc into the quadratic formula.\newlinez=(−(7)±(7)2−4(1)(4))/(2(1))z = (-(7) \pm \sqrt{(7)^2 - 4(1)(4)}) / (2(1))\newlinez=(−7±49−16)/2z = (-7 \pm \sqrt{49 - 16}) / 2\newlinez=(−7±33)/2z = (-7 \pm \sqrt{33}) / 2
  3. Simplify Equation: Simplify under the square root and the fraction.\newlinez=−7±332z = \frac{-7 \pm \sqrt{33}}{2}\newlineSince 33\sqrt{33} cannot be simplified further, we leave it as is.
  4. Calculate Possible Values: Calculate the two possible values for zz.\newlineFirst, calculate the addition part of the formula:\newlinez=−7+332z = \frac{-7 + \sqrt{33}}{2}\newlineNext, calculate the subtraction part of the formula:\newlinez=−7−332z = \frac{-7 - \sqrt{33}}{2}
  5. Round Decimal Values: Round the decimal values to the nearest hundredth if necessary. However, since the question asks for integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth, we will leave the answers in the form of fractions with the square root, as they cannot be simplified to integers or proper fractions.

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