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Solve using the quadratic formula.\newline9h2+9h+2=09h^2 + 9h + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____

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Q. Solve using the quadratic formula.\newline9h2+9h+2=09h^2 + 9h + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 9h2+9h+2=09h^2 + 9h + 2 = 0. The quadratic equation is in the form ah2+bh+c=0ah^2 + bh + c = 0, so by comparison: a=9a = 9 b=9b = 9 c=2c = 2
  2. Substitute formula: Substitute the values of aa, bb, and cc into the quadratic formula.\newlineThe quadratic formula is h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineSubstituting the values we get:\newlineh=−(9)±(9)2−4⋅9⋅22⋅9h = \frac{-(9) \pm \sqrt{(9)^2 - 4\cdot9\cdot2}}{2\cdot9}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant).\newlineCalculate the discriminant: (9)2−4⋅9⋅2(9)^2 - 4\cdot9\cdot2\newline= 81−7281 - 72\newline= 99
  4. Continue formula simplification: Continue simplifying the quadratic formula with the calculated discriminant.\newlineh=−9±918h = \frac{-9 \pm \sqrt{9}}{18}\newlineSince 9=3\sqrt{9} = 3, we have:\newlineh=−9±318h = \frac{-9 \pm 3}{18}
  5. Find possible values: Find the two possible values for hh.
    First solution:
    h=(−9+3)/18h = (-9 + 3) / 18
    h=−6/18h = -6 / 18
    h=−1/3h = -1/3
    Second solution:
    h=(−9−3)/18h = (-9 - 3) / 18
    h=−12/18h = -12 / 18
    h=−2/3h = -2/3
  6. Simplify fractions: Simplify the fractions and if necessary, round to the nearest hundredth. The fractions are already in simplest form, so rounding to the nearest hundredth is not necessary. h=−13h = -\frac{1}{3} or h=−23h = -\frac{2}{3}

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