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Solve using the quadratic formula.\newline8h2−5h−8=08h^2 - 5h - 8 = 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.\newline8h2−5h−8=08h^2 - 5h - 8 = 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 8h2−5h−8=08h^2 - 5h - 8 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=8a = 8 b=−5b = -5 c=−8c = -8
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find hh. The quadratic formula is h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: h=−(−5)±(−5)2−4⋅8⋅(−8)2⋅8h = \frac{-(-5) \pm \sqrt{(-5)^2 - 4\cdot8\cdot(-8)}}{2\cdot8}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (−5)2−4⋅8⋅(−8)=25+256=281\sqrt{(-5)^2 - 4 \cdot 8 \cdot (-8)} = \sqrt{25 + 256} = \sqrt{281}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the values found.\newlineh=5±28116h = \frac{5 \pm \sqrt{281}}{16}\newlineThis gives us two possible solutions for hh.
  5. Calculate possible values: Calculate the two possible values for hh.\newlineFirst solution:\newlineh=5+28116h = \frac{5 + \sqrt{281}}{16}\newlineSecond solution:\newlineh=5−28116h = \frac{5 - \sqrt{281}}{16}
  6. Round to nearest hundredth: Round the values of hh to the nearest hundredth, if necessary.\newlineFirst solution:\newlineh≈(5+16.76)/16h \approx (5 + 16.76) / 16\newlineh≈21.76/16h \approx 21.76 / 16\newlineh≈1.36h \approx 1.36\newlineSecond solution:\newlineh≈(5−16.76)/16h \approx (5 - 16.76) / 16\newlineh≈−11.76/16h \approx -11.76 / 16\newlineh≈−0.74h \approx -0.74

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