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Solve by completing the square.\newlinev2−8v=−15v^2 - 8v = -15\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.\newlinev2−8v=−15v^2 - 8v = -15\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: Write the equation in the form of v2+bv=cv^2 + bv = c. The given equation is v2−8v=−15v^2 - 8v = -15. We want to complete the square on the left side.
  2. Add 1515: Add 1515 to both sides to isolate the v2v^2 and vv terms on one side.\newlinev2−8v+15=−15+15v^2 - 8v + 15 = -15 + 15\newlinev2−8v+15=0v^2 - 8v + 15 = 0
  3. Find completion number: Find the number to complete the square.\newlineTo complete the square, we need to add (b/2)2(b/2)^2 to both sides, where bb is the coefficient of vv. In this case, b=−8b = -8, so (b/2)2=(−8/2)2=(−4)2=16(b/2)^2 = (-8/2)^2 = (-4)^2 = 16.
  4. Add 1616: Add 1616 to both sides to complete the square.\newlinev2−8v+16=0+16v^2 - 8v + 16 = 0 + 16\newline(v−4)2=16(v - 4)^2 = 16
  5. Take square root: Take the square root of both sides.\newline(v−4)2=±16\sqrt{(v - 4)^2} = \pm\sqrt{16}\newlinev−4=±4v - 4 = \pm4
  6. Solve for v: Solve for vv.v=4±4v = 4 \pm 4v=4+4v = 4 + 4 or v=4−4v = 4 - 4v=8v = 8 or v=0v = 0

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