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Solve by completing the square.\newlines2+16s=47s^2 + 16s = 47\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+16s=47s^2 + 16s = 47\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+16s=47s^2 + 16s = 47.
  2. Complete the Square: Add the square of half the coefficient of ss to both sides to complete the square.\newlineThe coefficient of ss is 1616, so half of it is 88, and the square of 88 is 6464.\newlineAdd 6464 to both sides of the equation:\newlines2+16s+64=47+64s^2 + 16s + 64 = 47 + 64\newlines2+16s+64=111s^2 + 16s + 64 = 111
  3. Factor Left Side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial:\newline(s+8)2=111(s + 8)^2 = 111
  4. Take Square Root: Take the square root of both sides of the equation.\newline(s+8)2=±111\sqrt{(s + 8)^2} = \pm\sqrt{111}\newlines+8=±111s + 8 = \pm\sqrt{111}
  5. Solve for ss: Solve for ss by isolating the variable.\newlineSubtract 88 from both sides of the equation:\newlines=−8±111s = -8 \pm \sqrt{111}
  6. Approximate and Solve: Approximate the square root of 111111 to the nearest hundredth and solve for ss.111≈10.54\sqrt{111} \approx 10.54s≈−8±10.54s \approx -8 \pm 10.54s≈−8+10.54s \approx -8 + 10.54 or s≈−8−10.54s \approx -8 - 10.54s≈2.54s \approx 2.54 or s≈−18.54s \approx -18.54

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