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Solve by completing the square.\newlineq2+30q−47=0q^2 + 30q - 47 = 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+30q−47=0q^2 + 30q - 47 = 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 equation: Rewrite the equation in the form of q2+bq=cq^2 + bq = c. Add 4747 to both sides to set the equation up for completing the square. q2+30q−47+47=0+47q^2 + 30q - 47 + 47 = 0 + 47 q2+30q=47q^2 + 30q = 47
  2. Add 4747: Choose the number to add to both sides to complete the square.\newlineSince (30/2)2=225(30/2)^2 = 225, add 225225 to both sides.\newlineq2+30q+225=47+225q^2 + 30q + 225 = 47 + 225\newlineq2+30q+225=272q^2 + 30q + 225 = 272
  3. Choose number to add: Factor the left side of the equation.\newlineq2+30q+225=272q^2 + 30q + 225 = 272\newline(q+15)2=272(q + 15)^2 = 272
  4. Factor left side: Take the square root of both sides of the equation. (q+15)2=±272\sqrt{(q + 15)^2} = \pm\sqrt{272} q+15=±272q + 15 = \pm\sqrt{272}
  5. Take square root: Isolate the variable qq.\newlineSubtract 1515 from both sides of the equation.\newlineq+15−15=±272−15q + 15 - 15 = \pm\sqrt{272} - 15\newlineq=−15±272q = -15 \pm \sqrt{272}
  6. Isolate variable: Simplify the square root and round to the nearest hundredth if necessary. 272\sqrt{272} is approximately 16.4916.49 when rounded to the nearest hundredth. q=−15±16.49q = -15 \pm 16.49
  7. Simplify square root: Find the two values of qq.q=−15+16.49q = -15 + 16.49 implies q≈1.49q \approx 1.49.q=−15−16.49q = -15 - 16.49 implies q≈−31.49q \approx -31.49.Values of qq: 1.491.49, −31.49-31.49

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