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Solve by completing the square.\newlines2−28s=13s^2 - 28s = 13\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____

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Q. Solve by completing the square.\newlines2−28s=13s^2 - 28s = 13\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____
  1. Write Equation Form: Write the equation in the form of s2+bs=cs^2 + bs = c. The given equation is already in this form: s2−28s=13s^2 - 28s = 13.
  2. Move Constant Term: Move the constant term to the other side of the equation.\newlineAdd 1313 to both sides to isolate the s2s^2 and ss terms.\newlines2−28s+13−13=13+13s^2 - 28s + 13 - 13 = 13 + 13\newlines2−28s=13s^2 - 28s = 13
  3. Find Completing Number: Find the number to complete the square.\newlineTo complete the square, we need to add (−282)2(-\frac{28}{2})^2 to both sides of the equation.\newline(−282)2=(−14)2=196(-\frac{28}{2})^2 = (-14)^2 = 196\newlines2−28s+196=13+196s^2 − 28s + 196 = 13 + 196\newlines2−28s+196=209s^2 − 28s + 196 = 209
  4. Factor Left Side: Factor the left side of the equation.\newlineThe left side of the equation is now a perfect square trinomial.\newline(s−14)2=209(s - 14)^2 = 209
  5. Take Square Root: Take the square root of both sides of the equation.\newline(s−14)2=±209\sqrt{(s - 14)^2} = \pm\sqrt{209}\newlines−14=±209s - 14 = \pm\sqrt{209}
  6. Solve for s: Solve for s.\newlineAdd 1414 to both sides of the equation to isolate ss.\newlines=14±209s = 14 \pm \sqrt{209}
  7. Calculate Decimal Values: Calculate the approximate decimal values of ss.209\sqrt{209} is approximately 14.4614.46 when rounded to the nearest hundredth.s≈14±14.46s \approx 14 \pm 14.46s≈14+14.46s \approx 14 + 14.46 or s≈14−14.46s \approx 14 - 14.46s≈28.46s \approx 28.46 or s≈−0.46s \approx -0.46

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