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Solve by completing the square.\newlineq2+28q−11=0q^2 + 28q - 11 = 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+28q−11=0q^2 + 28q - 11 = 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. Rewrite in standard form: q2+28q−11=0q^2 + 28q - 11 = 0\newlineRewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineAdd 1111 to both sides.\newlineq2+28q−11+11=0+11q^2 + 28q - 11 + 11 = 0 + 11\newlineq2+28q=11q^2 + 28q = 11
  2. Complete the square: q2+28q=11q^2 + 28q = 11\newlineChoose the equation after completing the square.\newlineSince (28/2)2=196(28/2)^2 = 196, add 196196 to both sides.\newlineq2+28q+196=11+196q^2 + 28q + 196 = 11 + 196\newlineq2+28q+196=207q^2 + 28q + 196 = 207
  3. Identify factored form: q2+28q+196=207q^2 + 28q + 196 = 207\newlineIdentify the equation after factoring the left side.\newlineq2+28q+196=207q^2 + 28q + 196 = 207\newline(q+14)2=207(q + 14)^2 = 207
  4. Take square root: (q+14)2=207(q + 14)^2 = 207\newlineIdentify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline(q+14)2=207\sqrt{(q + 14)^2} = \sqrt{207}\newlineq+14=±207q + 14 = \pm\sqrt{207}
  5. Isolate variable: We found:\newlineq+14=±207q + 14 = \pm\sqrt{207}\newlineChoose the equation after isolating the variable q.\newlineTo isolate q, subtract 1414 from both sides of the equation.\newlineq+14−14=±207−14q + 14 - 14 = \pm\sqrt{207} - 14\newlineq=−14±207q = -14 \pm \sqrt{207}
  6. Isolate variable: We found:\newlineq+14=±207q + 14 = \pm\sqrt{207}\newlineChoose the equation after isolating the variable qq.\newlineTo isolate qq, subtract 1414 from both sides of the equation.\newlineq+14−14=±207−14q + 14 - 14 = \pm\sqrt{207} - 14\newlineq=−14±207q = -14 \pm \sqrt{207}We have:\newlineq=−14±207q = -14 \pm \sqrt{207}\newlineWhat are the two values of qq?\newlineRound the non-terminating values to the nearest hundredth.\newlineq=−14+207q = -14 + \sqrt{207} implies q≈−14+14.39q \approx -14 + 14.39.\newlineqq00 implies qq11.\newlineValues of qq: qq33, qq44

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