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Solve by completing the square.\newliney2−26y=49y^2 - 26y = 49\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.\newliney2−26y=49y^2 - 26y = 49\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. Move Constant Term: Rewrite the equation in the form of y2+by=cy^2 + by = c. We have the equation y2−26y=49y^2 - 26y = 49. To complete the square, we need to move the constant term to the other side of the equation. y2−26y+___=49+___y^2 - 26y + \_\_\_ = 49 + \_\_\_
  2. Find Completing Number: Find the number to complete the square.\newlineTo complete the square, we need to add (−262)2(-\frac{26}{2})^2 to both sides of the equation. This is because the term we add to both sides must turn the left side into a perfect square trinomial.\newline(−262)2=(−13)2=169(-\frac{26}{2})^2 = (-13)^2 = 169\newlineSo, we add 169169 to both sides.\newliney2−26y+169=49+169y^2 - 26y + 169 = 49 + 169
  3. Rewrite as Binomial: Rewrite the equation as a squared binomial.\newlineNow that we have added 169169 to both sides, the left side of the equation is a perfect square trinomial.\newliney2−26y+169=218y^2 − 26y + 169 = 218\newlineThis can be factored into (y−13)2(y − 13)^2 because (y−13)(y−13)=y2−26y+169(y − 13)(y − 13) = y^2 − 26y + 169.\newline(y−13)2=218(y − 13)^2 = 218
  4. Take Square Root: Take the square root of both sides.\newlineTo solve for yy, we take the square root of both sides of the equation. Remember to consider both the positive and negative square roots.\newline(y−13)2=±218\sqrt{(y - 13)^2} = \pm\sqrt{218}\newliney−13=±218y - 13 = \pm\sqrt{218}
  5. Solve for y: Solve for y.\newlineNow we isolate yy by adding 1313 to both sides of the equation.\newliney=13±218y = 13 \pm \sqrt{218}\newlineSince 218\sqrt{218} is not a perfect square, we can approximate it to the nearest hundredth.\newline218≈14.76\sqrt{218} \approx 14.76\newliney≈13±14.76y \approx 13 \pm 14.76
  6. Find Values of y: Find the two values of y.\newlineWe have two possible solutions for y, one using the positive square root and one using the negative square root.\newliney≈13+14.76y \approx 13 + 14.76 implies y≈27.76y \approx 27.76.\newliney≈13−14.76y \approx 13 - 14.76 implies y≈−1.76y \approx -1.76.\newlineValues of y: 27.7627.76, −1.76-1.76

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