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Solve using the quadratic formula.\newlinep2+7p+9=0p^2 + 7p + 9 = 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.\newlinep2+7p+9=0p^2 + 7p + 9 = 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=0a p^2 + b p + c = 0. For the equation p2+7p+9=0p^2 + 7p + 9 = 0, the coefficients are:\newlinea = 11 (coefficient of p2p^2)\newlineb = 77 (coefficient of pp)\newlinec = 99 (constant term)
  2. Write formula: Write down the quadratic formula.\newlineThe quadratic formula is p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute coefficients: Substitute the coefficients into the quadratic formula.\newlineUsing the values of aa, bb, and cc from Step 11, we get:\newlinep=−(7)±(7)2−4(1)(9)2(1)p = \frac{-(7) \pm \sqrt{(7)^2 - 4(1)(9)}}{2(1)}
  4. Simplify square root: Simplify under the square root.\newlineCalculate the discriminant (the expression under the square root):\newline(7)2−4(1)(9)=49−36=13(7)^2 - 4(1)(9) = 49 - 36 = 13
  5. Insert discriminant: Insert the discriminant into the formula.\newlineNow we have:\newlinep=−7±132p = \frac{{-7 \pm \sqrt{13}}}{{2}}
  6. Write two solutions: Write down the two solutions.\newlineThe quadratic formula gives us two solutions, one for the plus sign and one for the minus sign:\newlinep=−7+132p = \frac{-7 + \sqrt{13}}{2} or p=−7−132p = \frac{-7 - \sqrt{13}}{2}
  7. Simplify solutions: Simplify the solutions if possible.\newlineThe square root of 1313 cannot be simplified further, and the fraction cannot be reduced. Therefore, the solutions are already in their simplest form.
  8. Round to nearest hundredth: Round the solutions to the nearest hundredth if necessary.\newlineSince the question asks for solutions as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth, we will provide the decimal approximations:\newlinep≈(−7+13)/2≈(−7+3.61)/2≈−3.39/2≈−1.70p \approx (-7 + \sqrt{13}) / 2 \approx (-7 + 3.61) / 2 \approx -3.39 / 2 \approx -1.70\newlinep≈(−7−13)/2≈(−7−3.61)/2≈−10.61/2≈−5.30p \approx (-7 - \sqrt{13}) / 2 \approx (-7 - 3.61) / 2 \approx -10.61 / 2 \approx -5.30

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