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Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____

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Q. Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
  1. Move constant term: We start with the equation m2−10m−29=0m^2 - 10m - 29 = 0 and move the constant term to the right side of the equation.\newlinem2−10m=29m^2 - 10m = 29
  2. Complete the square: To complete the square, we need to add (b2)2(\frac{b}{2})^2 to both sides of the equation, where bb is the coefficient of mm. In this case, b=−10b = -10, so (b2)2=(−102)2=25(\frac{b}{2})^2 = (\frac{-10}{2})^2 = 25.m2−10m+25=29+25m^2 − 10m + 25 = 29 + 25
  3. Simplify equation: Simplify both sides of the equation. m2−10m+25=54m^2 - 10m + 25 = 54
  4. Factor perfect square trinomial: Now, the left side of the equation is a perfect square trinomial, which can be factored into (m−5)2(m - 5)^2.(m−5)2=54(m - 5)^2 = 54
  5. Take square root: Take the square root of both sides of the equation to solve for mm.m−5=±54m - 5 = \pm\sqrt{54}
  6. Simplify square root: Simplify the square root of 5454. Since 54=9×654 = 9 \times 6 and 9=3\sqrt{9} = 3, we have 54=9×6=36\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}.\newlinem−5=±36m - 5 = \pm3\sqrt{6}
  7. Isolate mm: Add 55 to both sides of the equation to isolate mm.\newlinem=5±36m = 5 \pm 3\sqrt{6}
  8. Express as decimals: Now we can express the solutions as decimals rounded to the nearest hundredth. 6\sqrt{6} is approximately 2.452.45, so 363\sqrt{6} is approximately 3×2.45=7.353 \times 2.45 = 7.35.\newlinem≈5±7.35m \approx 5 \pm 7.35
  9. Calculate values: Calculate the two possible values for mm.m≈5+7.35≈12.35m \approx 5 + 7.35 \approx 12.35m≈5−7.35≈−2.35m \approx 5 - 7.35 \approx -2.35

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