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Solve by completing the square.\newlineq2+6q=23q^2 + 6q = 23\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____

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Q. Solve by completing the square.\newlineq2+6q=23q^2 + 6q = 23\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____
  1. Rewrite Equation: Rewrite the equation in the form of q2+bq=cq^2 + bq = c. We have the equation q2+6q=23q^2 + 6q = 23.
  2. Complete the Square: Add the square of half the coefficient of qq to both sides to complete the square.\newlineThe coefficient of qq is 66, so half of it is 33, and the square of 33 is 99.\newlineAdd 99 to both sides of the equation.\newlineq2+6q+9=23+9q^2 + 6q + 9 = 23 + 9\newlineq2+6q+9=32q^2 + 6q + 9 = 32
  3. Factor Left Side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(q+3)2=32(q + 3)^2 = 32
  4. Take Square Root: Take the square root of both sides of the equation.\newline(q+3)2=±32\sqrt{(q + 3)^2} = \pm\sqrt{32}\newlineq+3=±32q + 3 = \pm\sqrt{32}
  5. Solve for q: Solve for q.\newlineSubtract 33 from both sides of the equation.\newlineq=−3±32q = -3 \pm \sqrt{32}\newlineSince 32\sqrt{32} is approximately 5.665.66 when rounded to the nearest hundredth,\newlineq≈−3±5.66q \approx -3 \pm 5.66
  6. Find Values of q: Find the two values of q.\newlineq≈−3+5.66q \approx -3 + 5.66 implies q≈2.66q \approx 2.66.\newlineq≈−3−5.66q \approx -3 - 5.66 implies q≈−8.66q \approx -8.66.\newlineValues of q: 2.662.66, −8.66-8.66

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