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Solve by completing the square.\newlinem2−8m−5=0m^2 - 8m - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____

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Q. Solve by completing the square.\newlinem2−8m−5=0m^2 - 8m - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____
  1. Rewrite equation: Rewrite the equation in the form of m2+bm=cm^2 + bm = c. Add 55 to both sides to move the constant term to the right side of the equation. m2−8m−5+5=0+5m^2 - 8m - 5 + 5 = 0 + 5 m2−8m=5m^2 - 8m = 5
  2. Add constant term: Choose the number to add to both sides to complete the square.\newlineSince (−82)2=16(-\frac{8}{2})^2 = 16, add 1616 to both sides.\newlinem2−8m+16=5+16m^2 - 8m + 16 = 5 + 16\newlinem2−8m+16=21m^2 - 8m + 16 = 21
  3. Choose completing square number: Factor the left side of the equation.\newlinem2−8m+16=21m^2 - 8m + 16 = 21\newline(m−4)2=21(m - 4)^2 = 21
  4. Factor left side: Take the square root of both sides of the equation.\newline(m−4)2=21\sqrt{(m - 4)^2} = \sqrt{21}\newlinem−4=±21m - 4 = \pm\sqrt{21}
  5. Take square root: Solve for mm by isolating the variable.\newlineAdd 44 to both sides of the equation.\newlinem−4+4=±21+4m - 4 + 4 = \pm\sqrt{21} + 4\newlinem=4±21m = 4 \pm \sqrt{21}
  6. Solve for mm: Calculate the approximate decimal values of mm, rounded to the nearest hundredth.m≈4+21m \approx 4 + \sqrt{21} implies m≈4+4.58m \approx 4 + 4.58 which is m≈8.58m \approx 8.58.m≈4−21m \approx 4 - \sqrt{21} implies m≈4−4.58m \approx 4 - 4.58 which is m≈−0.58m \approx -0.58.

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