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Solve by completing the square.\newlinek2+20k=23k^2 + 20k = 23\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____

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Q. Solve by completing the square.\newlinek2+20k=23k^2 + 20k = 23\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____
  1. Write Equation Form: Write the equation in the form of k2+bk=ck^2 + bk = c. The given equation is already in this form: k2+20k=23k^2 + 20k = 23.
  2. Move Constant Term: Move the constant term to the right side of the equation.\newlineSubtract 2323 from both sides to isolate the kk terms.\newlinek2+20k−23=0k^2 + 20k - 23 = 0\newlinek2+20k=23k^2 + 20k = 23
  3. Complete Square: Complete the square by adding the square of half the coefficient of kk to both sides.\newlineThe coefficient of kk is 2020, so half of it is 1010. The square of 1010 is 100100.\newlineAdd 100100 to both sides of the equation.\newlinek2+20k+100=23+100k^2 + 20k + 100 = 23 + 100\newlinek2+20k+100=123k^2 + 20k + 100 = 123
  4. Factor Perfect Square: Factor the left side of the equation as a perfect square. The left side is now a perfect square trinomial. (k+10)2=123(k + 10)^2 = 123
  5. Take Square Root: Take the square root of both sides of the equation.\newline(k+10)2=±123\sqrt{(k + 10)^2} = \pm\sqrt{123}\newlinek+10=±123k + 10 = \pm\sqrt{123}
  6. Solve for k: Solve for k by isolating the variable.\newlineSubtract 1010 from both sides of the equation.\newlinek=−10±123k = -10 \pm \sqrt{123}
  7. Simplify Square Root: Simplify the square root if possible and round to the nearest hundredth if necessary.123\sqrt{123} is not a perfect square, so we will use a calculator to approximate the value.123≈11.09\sqrt{123} \approx 11.09k≈−10±11.09k \approx -10 \pm 11.09
  8. Find Values of k: Find the two values of kk.k≈−10+11.09k \approx -10 + 11.09 implies k≈1.09k \approx 1.09.k≈−10−11.09k \approx -10 - 11.09 implies k≈−21.09k \approx -21.09.Values of kk: 1.091.09, −21.09-21.09

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