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Solve by completing the square.\newlinev2−4v−43=0v^2 - 4v - 43 = 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.\newlinev2−4v−43=0v^2 - 4v - 43 = 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 Equation: Rewrite the equation in the form of v2+bv=cv^2 + bv = c. Add 4343 to both sides to set the equation up for completing the square. v2−4v−43+43=0+43v^2 - 4v - 43 + 43 = 0 + 43 v2−4v=43v^2 - 4v = 43
  2. Add 4343: Choose the number to add to both sides to complete the square.\newlineSince (−42)2=4\left(-\frac{4}{2}\right)^2 = 4, add 44 to both sides.\newlinev2−4v+4=43+4v^2 - 4v + 4 = 43 + 4\newlinev2−4v+4=47v^2 - 4v + 4 = 47
  3. Complete the Square: Factor the left side of the equation.\newlinev2−4v+4v^2 - 4v + 4 is a perfect square trinomial.\newline(v−2)2=47(v - 2)^2 = 47
  4. Factor Trinomial: Take the square root of both sides of the equation.\newline(v−2)2=±47\sqrt{(v - 2)^2} = \pm\sqrt{47}\newlinev−2=±47v - 2 = \pm\sqrt{47}
  5. Take Square Root: Solve for vv.\newlineAdd 22 to both sides of the equation to isolate vv.\newlinev−2+2=±47+2v - 2 + 2 = \pm\sqrt{47} + 2\newlinev=2±47v = 2 \pm \sqrt{47}
  6. Solve for vv: Calculate the approximate decimal values of vv.\newlinev≈2+47v \approx 2 + \sqrt{47} or v≈2−47v \approx 2 - \sqrt{47}\newlinev≈2+6.86v \approx 2 + 6.86 or v≈2−6.86v \approx 2 - 6.86\newlinev≈8.86v \approx 8.86 or v≈−4.86v \approx -4.86\newlineRound to the nearest hundredth.

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