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Solve using the quadratic formula.\newline2h2−5h−1=02h^2 - 5h - 1 = 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.\newline2h2−5h−1=02h^2 - 5h - 1 = 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 2h2−5h−1=02h^2 - 5h - 1 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=2a = 2 b=−5b = -5 c=−1c = -1
  2. Substitute in 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⋅2⋅(−1)2⋅2h = \frac{-(-5) \pm \sqrt{(-5)^2 - 4\cdot2\cdot(-1)}}{2\cdot2}
  3. Simplify expression: Simplify the expression under the square root and the constants outside the square root.\newlineh=5±25−(−8)4h = \frac{5 \pm \sqrt{25 - (-8)}}{4}\newlineh=5±25+84h = \frac{5 \pm \sqrt{25 + 8}}{4}\newlineh=5±334h = \frac{5 \pm \sqrt{33}}{4}
  4. Identify possible values: Identify the two possible values for hh.h=5+334h = \frac{5 + \sqrt{33}}{4} or h=5−334h = \frac{5 - \sqrt{33}}{4}
  5. Round to nearest hundredth: If necessary, round the values of hh to the nearest hundredth.\newlineh≈(5+5.74)/4h \approx (5 + 5.74) / 4 or h≈(5−5.74)/4h \approx (5 - 5.74) / 4\newlineh≈10.74/4h \approx 10.74 / 4 or h≈−0.74/4h \approx -0.74 / 4\newlineh≈2.685h \approx 2.685 or h≈−0.185h \approx -0.185

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