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Solve using the quadratic formula.\newline3h2−7h−4=03h^2 - 7h - 4 = 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.\newline3h2−7h−4=03h^2 - 7h - 4 = 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 3h2−7h−4=03h^2 - 7h - 4 = 0. The quadratic equation is in the form ah2+bh+c=0ah^2 + bh + c = 0. For our equation, a=3a = 3, b=−7b = -7, and c=−4c = -4.
  2. Substitute into formula: Substitute the values of aa, bb, and cc into the quadratic formula h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, h=−(−7)±(−7)2−4⋅3⋅(−4)2⋅3h = \frac{-(-7) \pm \sqrt{(-7)^2 - 4\cdot3\cdot(-4)}}{2\cdot3}.
  3. Simplify terms: Simplify the terms inside the square root and the constants outside the square root.\newlineh=7±49+486h = \frac{7 \pm \sqrt{49 + 48}}{6}.\newlineh=7±976h = \frac{7 \pm \sqrt{97}}{6}.
  4. Calculate square root: Calculate the square root of 9797 to determine the two possible values for hh.97\sqrt{97} is an irrational number, so we will use it as is for the exact solution and then approximate it for the decimal solution.
  5. Write possible solutions: Write the two possible solutions for hh.h=7+976h = \frac{7 + \sqrt{97}}{6} or h=7−976h = \frac{7 - \sqrt{97}}{6}.
  6. Round values: If necessary, round the values of hh to the nearest hundredth.\newlineh≈(7+9.85)/6h \approx (7 + 9.85) / 6 or h≈(7−9.85)/6h \approx (7 - 9.85) / 6.\newlineh≈16.85/6h \approx 16.85 / 6 or h≈−2.85/6h \approx -2.85 / 6.\newlineh≈2.81h \approx 2.81 or h≈−0.48h \approx -0.48.

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