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Solve by completing the square.\newlinev2+20v−39=0v^2 + 20v - 39 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____

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Q. Solve by completing the square.\newlinev2+20v−39=0v^2 + 20v - 39 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____
  1. Rewrite in standard form: v2+20v−39=0v^2 + 20v - 39 = 0\newlineRewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineAdd 3939 to both sides to set the equation up for completing the square.\newlinev2+20v−39+39=0+39v^2 + 20v - 39 + 39 = 0 + 39\newlinev2+20v=39v^2 + 20v = 39
  2. Add 3939 to both sides: v2+20v=39v^2 + 20v = 39\newlineChoose the number to add to both sides to complete the square.\newlineSince (20/2)2=100(20/2)^2 = 100, add 100100 to both sides.\newlinev2+20v+100=39+100v^2 + 20v + 100 = 39 + 100\newlinev2+20v+100=139v^2 + 20v + 100 = 139
  3. Complete the square: v2+20v+100=139v^2 + 20v + 100 = 139\newlineIdentify the equation after factoring the left side.\newlinev2+20v+100=139v^2 + 20v + 100 = 139\newline(v+10)2=139(v + 10)^2 = 139
  4. Identify factored form: v+10)2=139(v + 10)^2 = 139(\newlineIdentify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline\$\sqrt{(v + 10)^2} = \sqrt{139}\)\(\newline\)\(v + 10 = \pm\sqrt{139}\)
  5. Take square root: We found:\(\newline\)\(v + 10 = \pm\sqrt{139}\)\(\newline\)Choose the equation after isolating the variable \(v\).\(\newline\)To isolate \(v\), subtract \(10\) from both sides of the equation.\(\newline\)\(v + 10 - 10 = \pm\sqrt{139} - 10\)\(\newline\)\(v = -10 \pm \sqrt{139}\)
  6. Isolate variable: We have:\(\newline\)\(v = -10 \pm \sqrt{139}\)\(\newline\)What are the two values of \(v\)?\(\newline\)\(v = -10 + \sqrt{139}\) and \(v = -10 - \sqrt{139}\)\(\newline\)Round the non-terminating values to the nearest hundredth.\(\newline\)\(v \approx -10 + 11.79\) implies \(v \approx 1.79\).\(\newline\)\(v \approx -10 - 11.79\) implies \(v \approx -21.79\).\(\newline\)Values of \(v\): \(1.79\), \(v\)\(0\)

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