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Solve by completing the square.\newliney2−4y=25y^2 - 4y = 25\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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Q. Solve by completing the square.\newliney2−4y=25y^2 - 4y = 25\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Rewrite in standard form: Write the equation in the form of y2+by=cy^2 + by = c. The given equation is y2−4y=25y^2 - 4y = 25.
  2. Move constant term: Move the constant term to the other side of the equation.\newlineSubtract 2525 from both sides to isolate the yy terms.\newliney2−4y−25=0y^2 - 4y - 25 = 0\newliney2−4y=−25y^2 - 4y = -25
  3. Complete the square: Complete the square by adding the square of half the coefficient of yy to both sides.\newlineThe coefficient of yy is −4-4, so half of that is −2-2, and the square of −2-2 is 44.\newlineAdd 44 to both sides of the equation.\newliney2−4y+4=−25+4y^2 - 4y + 4 = -25 + 4\newliney2−4y+4=−21y^2 - 4y + 4 = -21
  4. Factor left side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(y−2)2=−21(y - 2)^2 = -21
  5. Take square root: Take the square root of both sides of the equation.\newlineRemember to include the ±\pm symbol when taking the square root of both sides.\newline(y−2)2=±−21\sqrt{(y - 2)^2} = \pm\sqrt{-21}\newliney−2=±−21y - 2 = \pm\sqrt{-21}
  6. No real solutions: Since the square root of a negative number is not a real number, there are no real solutions to this equation.\newlineThe equation y2−4y=25y^2 - 4y = 25 does not have real solutions because you cannot take the square root of a negative number in the real number system.

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