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Solve by completing the square.\newlineq2−18q=37q^2 - 18q = 37\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.\newlineq2−18q=37q^2 - 18q = 37\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. Write Equation Form: Write the equation in the form of q2+bq=cq^2 + bq = c. The given equation is q2−18q=37q^2 - 18q = 37.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineAdd 3737 to both sides to isolate the q2q^2 and qq terms.\newlineq2−18q+37−37=37+37q^2 - 18q + 37 - 37 = 37 + 37\newlineq2−18q=37q^2 - 18q = 37
  3. Complete the Square: Complete the square by adding (b2)2(\frac{b}{2})^2 to both sides of the equation.\newlineSince b=−18b = -18 in the equation q2−18qq^2 − 18q, we calculate (−182)2=81(\frac{-18}{2})^2 = 81.\newlineAdd 8181 to both sides of the equation.\newlineq2−18q+81=37+81q^2 − 18q + 81 = 37 + 81\newlineq2−18q+81=118q^2 − 18q + 81 = 118
  4. Factor Perfect Square: Factor the left side of the equation as a perfect square. The left side of the equation is now a perfect square trinomial. (q−9)2=118(q - 9)^2 = 118
  5. Take Square Root: Take the square root of both sides of the equation.\newlineTo solve for qq, take the square root of both sides.\newline(q−9)2=±118\sqrt{(q - 9)^2} = \pm\sqrt{118}\newlineq−9=±118q - 9 = \pm\sqrt{118}
  6. Solve for q: Solve for q by isolating the variable.\newlineAdd 99 to both sides of the equation to isolate qq.\newlineq−9+9=±118+9q - 9 + 9 = \pm\sqrt{118} + 9\newlineq=9±118q = 9 \pm \sqrt{118}
  7. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary. 118\sqrt{118} is approximately 10.8610.86 when rounded to the nearest hundredth. q=9±10.86q = 9 \pm 10.86
  8. Find q Values: Find the two values of q.\newlineq=9+10.86q = 9 + 10.86 or q=9−10.86q = 9 - 10.86\newlineq≈19.86q \approx 19.86 or q≈−1.86q \approx -1.86

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