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Solve by completing the square.\newlinep2−6p−11=0p^2 - 6p - 11 = 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 by completing the square.\newlinep2−6p−11=0p^2 - 6p - 11 = 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. Rewrite Equation: Rewrite the equation in the form of p2+bp=cp^2 + bp = c.\newlineAdd 1111 to both sides to move the constant term to the right side of the equation.\newlinep2−6p−11+11=0+11p^2 - 6p - 11 + 11 = 0 + 11\newlinep2−6p=11p^2 - 6p = 11
  2. Complete the Square: Choose the number to add to both sides to complete the square.\newlineSince (−62)2=9(-\frac{6}{2})^2 = 9, add 99 to both sides.\newlinep2−6p+9=11+9p^2 − 6p + 9 = 11 + 9\newlinep2−6p+9=20p^2 − 6p + 9 = 20
  3. Factor Left Side: Factor the left side of the equation.\newlinep2−6p+9=20p^2 - 6p + 9 = 20\newline(p−3)2=20(p - 3)^2 = 20
  4. Take Square Root: Take the square root of both sides of the equation.\newline(p−3)2=±20\sqrt{(p − 3)^2} = \pm\sqrt{20}\newlinep−3=±20p − 3 = \pm\sqrt{20}
  5. Isolate Variable: Isolate the variable pp.\newlineTo isolate pp, add 33 to both sides of the equation.\newlinep−3+3=±20+3p - 3 + 3 = \pm\sqrt{20} + 3\newlinep = 3±203 \pm \sqrt{20}
  6. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary. 20\sqrt{20} can be simplified to 252\sqrt{5}, which is approximately 4.474.47 when rounded to the nearest hundredth. p=3±4.47p = 3 \pm 4.47
  7. Find Values: Find the two values of pp.p=3+4.47p = 3 + 4.47 implies p≈7.47p \approx 7.47.p=3−4.47p = 3 - 4.47 implies p≈−1.47p \approx -1.47.Values of pp: 7.477.47, −1.47-1.47

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