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Solve using the quadratic formula.\newline6p2−7p−8=06p^2 - 7p - 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____

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Q. Solve using the quadratic formula.\newline6p2−7p−8=06p^2 - 7p - 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 6p2−7p−8=06p^2 − 7p − 8 = 0.a=6a = 6, b=−7b = -7, c=−8c = -8
  2. Write quadratic formula: Write down the quadratic formula: p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.p=−(−7)±(−7)2−4⋅6⋅(−8)2⋅6p = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 6 \cdot (-8)}}{2 \cdot 6}
  4. Simplify expression: Simplify the expression inside the square root: (−7)2−4⋅6⋅(−8)=49+192=241\sqrt{(-7)^2 - 4\cdot6\cdot(-8)} = \sqrt{49 + 192} = \sqrt{241}
  5. Insert simplified values: Insert the simplified square root back into the formula and simplify the constants.\newlinep=7±24112p = \frac{7 \pm \sqrt{241}}{12}
  6. Calculate possible solutions: Calculate the two possible solutions for pp.p=7+24112p = \frac{7 + \sqrt{241}}{12} or p=7−24112p = \frac{7 - \sqrt{241}}{12}
  7. Round values: Round the values of pp to the nearest hundredth, if necessary.p≈(7+15.52)/12p \approx (7 + 15.52) / 12 or p≈(7−15.52)/12p \approx (7 - 15.52) / 12p≈22.52/12p \approx 22.52 / 12 or p≈−8.52/12p \approx -8.52 / 12p≈1.88p \approx 1.88 or p≈−0.71p \approx -0.71

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