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Solve using the quadratic formula.\newline6p2+3p−2=06p^2 + 3p - 2 = 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+3p−2=06p^2 + 3p - 2 = 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 values: Identify the values of aa, bb, and cc from the quadratic equation 6p2+3p−2=06p^2 + 3p - 2 = 0. Compare 6p2+3p−2=06p^2 + 3p - 2 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=6a = 6 b=3b = 3 c=−2c = -2
  2. Substitute into formula: Substitute the values of aa, bb, and cc into the quadratic formula p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=6a = 6, b=3b = 3, and c=−2c = -2 into the quadratic formula. p=−(3)±(3)2−4⋅6⋅(−2)2⋅6p = \frac{-(3) \pm \sqrt{(3)^2 - 4\cdot6\cdot(-2)}}{2\cdot6}
  3. Simplify and calculate: Simplify the expression under the square root and calculate the discriminant.\newline(3)2−4⋅6⋅(−2)\sqrt{(3)^2 - 4\cdot 6\cdot (-2)}\newline= 9+48\sqrt{9 + 48}\newline= 57\sqrt{57}
  4. Calculate solutions: Calculate the two possible solutions for pp.p=−3±572⋅6p = \frac{-3 \pm \sqrt{57}}{2\cdot6}p=−3±5712p = \frac{-3 \pm \sqrt{57}}{12}p=−3+5712p = \frac{-3 + \sqrt{57}}{12} or p=−3−5712p = \frac{-3 - \sqrt{57}}{12}
  5. Round and approximate: Simplify the solutions and round to the nearest hundredth if necessary.\newlinep=−3+5712p = \frac{-3 + \sqrt{57}}{12} or p=−3−5712p = \frac{-3 - \sqrt{57}}{12}\newlineSince 57\sqrt{57} is approximately 7.557.55, we can approximate the solutions.\newlinep≈−3+7.5512p \approx \frac{-3 + 7.55}{12} or p≈−3−7.5512p \approx \frac{-3 - 7.55}{12}\newlinep≈4.5512p \approx \frac{4.55}{12} or p≈−10.5512p \approx \frac{-10.55}{12}\newlinep≈0.38p \approx 0.38 or p≈−0.88p \approx -0.88

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