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Solve by completing the square.\newlineq2−18q=−43q^2 - 18q = -43\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=−43q^2 - 18q = -43\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 and Add Constant: Rewrite the equation in the form of q2+bq=cq^2 + bq = c. Add 4343 to both sides to move the constant term to the right side of the equation. q2−18q+43=−43+43q^2 - 18q + 43 = -43 + 43 q2−18q=43q^2 - 18q = 43
  2. Choose Number to Complete Square: Choose the number to add to both sides to complete the square.\newlineSince (−182)2=81\left(-\frac{18}{2}\right)^2 = 81, add 8181 to both sides.\newlineq2−18q+81=43+81q^2 − 18q + 81 = 43 + 81\newlineq2−18q+81=124q^2 − 18q + 81 = 124
  3. Factor Left Side: Factor the left side of the equation.\newlineq2−18q+81=124q^2 - 18q + 81 = 124\newline(q−9)2=124(q - 9)^2 = 124
  4. Take Square Root: Take the square root of both sides of the equation.\newline(q−9)2=124\sqrt{(q - 9)^2} = \sqrt{124}\newlineq−9=±124q - 9 = \pm\sqrt{124}
  5. Solve for q: Solve for q by isolating the variable.\newlineAdd 99 to both sides of the equation.\newlineq−9+9=±124+9q - 9 + 9 = \pm\sqrt{124} + 9\newlineq=9±124q = 9 \pm \sqrt{124}
  6. Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary. 124\sqrt{124} is approximately 11.1411.14. q=9±11.14q = 9 \pm 11.14
  7. Find Values of q: Find the two values of q.\newlineq=9+11.14q = 9 + 11.14 implies q≈20.14q \approx 20.14.\newlineq=9−11.14q = 9 - 11.14 implies q≈−2.14q \approx -2.14.\newlineValues of q: 20.1420.14, −2.14-2.14

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