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Solve using the quadratic formula.\newline5p2−3p−8=05p^2 - 3p - 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.\newline5p2−3p−8=05p^2 - 3p - 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 of the quadratic equation.\newlineThe quadratic equation is in the form ap2+bp+c=0ap^2 + bp + c = 0. For the equation 5p2−3p−8=05p^2 - 3p - 8 = 0, the coefficients are:\newlinea = 55\newlineb = −3-3\newlinec = −8-8
  2. Substitute into Formula: Substitute the coefficients into the quadratic formula.\newlineThe quadratic formula is p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get:\newlinep=−(−3)±(−3)2−4⋅5⋅(−8)2⋅5p = \frac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot5\cdot(-8)}}{2\cdot5}\newlinep=3±9+16010p = \frac{3 \pm \sqrt{9 + 160}}{10}
  3. Simplify Square Root: Simplify under the square root.\newlineCalculate the value inside the square root: 9+160=169\sqrt{9 + 160} = \sqrt{169}
  4. Simplify Root: Simplify the square root.\newlineSince 169\sqrt{169} is a perfect square, we find that:\newline169=13\sqrt{169} = 13
  5. Calculate Solutions: Calculate the two possible solutions for pp.\newlineNow we have two possible solutions for pp:\newlinep=3+1310p = \frac{3 + 13}{10} or p=3−1310p = \frac{3 - 13}{10}\newlinep=1610p = \frac{16}{10} or p=−1010p = \frac{-10}{10}
  6. Simplify Fractions: Simplify the fractions.\newlineSimplify the fractions to get the solutions in simplest form:\newlinep=85p = \frac{8}{5} or p=−1p = -1
  7. Convert to Decimal: Convert to decimal if necessary.\newlineIf we need the solutions as decimals rounded to the nearest hundredth:\newlinep≈1.60p \approx 1.60 or p=−1.00p = -1.00

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