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Solve using the quadratic formula.\newline7h2+3h−9=07h^2 + 3h - 9 = 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.\newline7h2+3h−9=07h^2 + 3h - 9 = 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 coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 7h2+3h−9=07h^2 + 3h - 9 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.a=7a = 7, b=3b = 3, c=−9c = -9
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula, h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineh=−(3)±(3)2−4(7)(−9)2(7)h = \frac{-(3) \pm \sqrt{(3)^2 - 4(7)(-9)}}{2(7)}
  3. Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Discriminant = (3)2−4(7)(−9)=9+252=261(3)^2 - 4(7)(-9) = 9 + 252 = 261
  4. Insert discriminant: Insert the discriminant back into the quadratic formula and simplify.\newlineh=−3±2612(7)h = \frac{-3 \pm \sqrt{261}}{2(7)}\newlineh=−3±26114h = \frac{-3 \pm \sqrt{261}}{14}
  5. Calculate solutions: Calculate the two possible solutions for hh by considering both the positive and negative square roots.\newlineh=−3+26114h = \frac{-3 + \sqrt{261}}{14} or h=−3−26114h = \frac{-3 - \sqrt{261}}{14}
  6. Round values: Round the values of hh to the nearest hundredth, if necessary.h≈(−3+16.1614)h \approx (\frac{-3 + 16.16}{14}) or h≈(−3−16.1614)h \approx (\frac{-3 - 16.16}{14})h≈13.1614h \approx \frac{13.16}{14} or h≈−19.1614h \approx \frac{-19.16}{14}h≈0.94h \approx 0.94 or h≈−1.37h \approx -1.37

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