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Solve by completing the square.\newlinep2+4p=13p^2 + 4p = 13\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+4p=13p^2 + 4p = 13\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. We have the equation p2+4p=13p^2 + 4p = 13. To complete the square, we need to have a constant term on the left side that makes it a perfect square trinomial.
  2. Add Constant Term: Add the square of half the coefficient of pp to both sides.\newlineThe coefficient of pp is 44, so half of it is 22. The square of 22 is 44.\newlineAdd 44 to both sides to complete the square.\newlinep2+4p+4=13+4p^2 + 4p + 4 = 13 + 4\newlinep2+4p+4=17p^2 + 4p + 4 = 17
  3. Factor and Simplify: Factor the left side as a binomial square and simplify the right side.\newlineThe left side is now a perfect square trinomial and can be factored as (p+2)2(p + 2)^2.\newline(p+2)2=17(p + 2)^2 = 17
  4. Take Square Root: Take the square root of both sides.\newlineTo solve for pp, we take the square root of both sides.\newline(p+2)2=±17\sqrt{(p + 2)^2} = \pm\sqrt{17}\newlinep+2=±17p + 2 = \pm\sqrt{17}
  5. Isolate Variable: Solve for pp by isolating the variable.\newlineSubtract 22 from both sides to isolate pp.\newlinep=−2±17p = -2 \pm \sqrt{17}
  6. Calculate Approximate Values: Calculate the approximate decimal values of pp, if necessary.\newlineSince 17\sqrt{17} is approximately 4.124.12, we can find the approximate values of pp.\newlinep≈−2+4.12p \approx -2 + 4.12 or p≈−2−4.12p \approx -2 - 4.12\newlinep≈2.12p \approx 2.12 or p≈−6.12p \approx -6.12

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