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Solve using the quadratic formula.\newline6p2−6p−4=06p^2 - 6p - 4 = 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.\newline6p2−6p−4=06p^2 - 6p - 4 = 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. Plug Values into Formula: Plug the values of aa, bb, and cc into the quadratic formula p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.p=−(−6)±(−6)2−4⋅6⋅(−4)2⋅6p = \frac{-(-6) \pm \sqrt{(-6)^2 - 4\cdot6\cdot(-4)}}{2\cdot6}.
  2. Simplify Equation: Simplify the equation. p=6±36+9612p = \frac{6 \pm \sqrt{36 + 96}}{12}.
  3. Add Inside Square Root: Continue simplifying by adding inside the square root. p=6±13212p = \frac{6 \pm \sqrt{132}}{12}.
  4. Simplify Square Root: Simplify 132\sqrt{132} to its simplest radical form.132=4×33=2×33\sqrt{132} = \sqrt{4\times33} = 2\times\sqrt{33}.
  5. Substitute Back into Equation: Substitute the simplified square root back into the equation. p=6±23312p = \frac{6 \pm 2\sqrt{33}}{12}.
  6. Divide by Denominator: Divide both terms in the numerator by the denominator.\newlinep=12±(16)33p = \frac{1}{2} \pm \left(\frac{1}{6}\right)\sqrt{33}.
  7. Round to Nearest Hundredth: Round the decimal part of the solutions to the nearest hundredth if necessary.\newlinep≈0.5±0.1733p \approx 0.5 \pm 0.17\sqrt{33}.\newlinep≈0.5±0.17⋅5.74p \approx 0.5 \pm 0.17\cdot5.74.
  8. Calculate Approximate Values: Calculate the approximate decimal values.\newlinep≈0.5+0.98p \approx 0.5 + 0.98 or p≈0.5−0.98p \approx 0.5 - 0.98.\newlinep≈1.48p \approx 1.48 or p≈−0.48p \approx -0.48.

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