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Solve using the quadratic formula.\newline9p2+9p−4=09p^2 + 9p - 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.\newline9p2+9p−4=09p^2 + 9p - 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. Identify coefficients: Identify the coefficients of the quadratic equation 9p2+9p−4=09p^2 + 9p - 4 = 0. Comparing 9p2+9p−4=09p^2 + 9p - 4 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=9a = 9 b=9b = 9 c=−4c = -4
  2. Substitute values 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=9a = 9, b=9b = 9, and c=−4c = -4 into the quadratic formula. p=−(9)±(9)2−4⋅9⋅(−4)2⋅9p = \frac{-(9) \pm \sqrt{(9)^2 - 4\cdot9\cdot(-4)}}{2\cdot9}
  3. Simplify discriminant: Simplify the expression under the square root, known as the discriminant.\newlineCalculate (9)2−4⋅9⋅(−4)\sqrt{(9)^2 - 4\cdot 9\cdot (-4)}.\newline(9)2−4⋅9⋅(−4)=81+144=225\sqrt{(9)^2 - 4\cdot 9\cdot (-4)} = \sqrt{81 + 144} = \sqrt{225}
  4. Simplify square root: Simplify the square root of the discriminant. 225=15\sqrt{225} = 15
  5. Substitute back into formula: Substitute the value of the square root back into the quadratic formula.\newlinep=(−(9)±15)/(2⋅9)p = (-(9) \pm 15) / (2\cdot9)\newlineCalculate the two possible solutions for pp.\newlinep=(−9+15)/18p = (-9 + 15) / 18 or p=(−9−15)/18p = (-9 - 15) / 18
  6. Simplify possible solutions: Simplify the two possible solutions for pp.p=618p = \frac{6}{18} or p=−2418p = \frac{-24}{18}Reduce the fractions to their simplest form.p=13p = \frac{1}{3} or p=−43p = \frac{-4}{3}
  7. Round if necessary: If necessary, round the values of pp to the nearest hundredth.p=0.33p = 0.33 or p=−1.33p = -1.33

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