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Solve by completing the square.\newlineq2−22q+21=0q^2 - 22q + 21 = 0\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.\newlineq2−22q+21=0q^2 - 22q + 21 = 0\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.\newlineSubtract 2121 from both sides to set the equation up for completing the square.\newlineq2−22q+21−21=0−21q^2 - 22q + 21 - 21 = 0 - 21\newlineq2−22q=−21q^2 - 22q = -21
  2. Subtract 2121: Find the number to add to both sides to complete the square.\newlineSince (−222)2=121(-\frac{22}{2})^2 = 121, add 121121 to both sides.\newlineq2−22q+121=−21+121q^2 − 22q + 121 = -21 + 121\newlineq2−22q+121=100q^2 − 22q + 121 = 100
  3. Find Number to Add: Factor the left side of the equation.\newlineq2−22q+121q^2 - 22q + 121 is a perfect square trinomial.\newline(q−11)2=100(q - 11)^2 = 100
  4. Factor Left Side: Take the square root of both sides of the equation.\newline(q−11)2=100\sqrt{(q - 11)^2} = \sqrt{100}\newlineq−11=±10q - 11 = \pm10
  5. Take Square Root: Solve for qq by isolating the variable.\newlineAdd 1111 to both sides of the equation.\newlineq−11+11=±10+11q - 11 + 11 = \pm 10 + 11\newlineq=11±10q = 11 \pm 10
  6. Solve for qq: Find the two values of qq.q=11+10q = 11 + 10 implies q=21q = 21.q=11−10q = 11 - 10 implies q=1q = 1.Values of qq: 2121, 11

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