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Solve by completing the square.\newlinep2+28p=39p^2 + 28p = 39\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+28p=39p^2 + 28p = 39\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+28p=39p^2 + 28p = 39.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineSubtract 3939 from both sides to isolate the p2p^2 and 28p28p terms.\newlinep2+28p−39=0p^2 + 28p - 39 = 0\newlinep2+28p=39p^2 + 28p = 39
  3. Complete the Square: Complete the square by adding the square of half the coefficient of pp to both sides.\newlineThe coefficient of pp is 2828, so half of it is 1414, and the square of 1414 is 196196.\newlinep2+28p+196=39+196p^2 + 28p + 196 = 39 + 196
  4. Factor and Simplify: Factor the left side of the equation and simplify the right side.\newline(p+14)2=235(p + 14)^2 = 235
  5. Take Square Root: Take the square root of both sides of the equation.\newline(p+14)2=±235\sqrt{(p + 14)^2} = \pm\sqrt{235}\newlinep+14=±235p + 14 = \pm\sqrt{235}
  6. Solve for p: Solve for p by subtracting 1414 from both sides.\newlinep=−14±235p = -14 \pm \sqrt{235}
  7. Calculate Approximate Values: Calculate the approximate decimal values of pp, rounded to the nearest hundredth.235≈15.33\sqrt{235} \approx 15.33p≈−14+15.33p \approx -14 + 15.33 or p≈−14−15.33p \approx -14 - 15.33p≈1.33p \approx 1.33 or p≈−29.33p \approx -29.33

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