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Solve by completing the square.\newlinem2+18m=−11m^2 + 18m = -11\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+18m=−11m^2 + 18m = -11\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. We have the equation m2+18m=−11m^2 + 18m = -11. To complete the square, we need to move the constant term to the other side. Add 1111 to both sides of the equation. m2+18m+11=−11+11m^2 + 18m + 11 = -11 + 11 m2+18m+11=0m^2 + 18m + 11 = 0
  2. Move constant term: Choose the equation after completing the square.\newlineSince (182)2=81(\frac{18}{2})^2 = 81, add 8181 to both sides to complete the square.\newlinem2+18m+81=11+81m^2 + 18m + 81 = 11 + 81\newlinem2+18m+81=92m^2 + 18m + 81 = 92
  3. Complete the square: Identify the equation after factoring the left side.\newlineThe left side is a perfect square trinomial.\newline(m+9)2=92(m + 9)^2 = 92
  4. Choose completed equation: Identify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline(m+9)2=±92\sqrt{(m + 9)^2} = \pm\sqrt{92}\newlinem + 99 = ±92\pm\sqrt{92}
  5. Factor left side: Choose the equation after isolating the variable mm. To isolate mm, subtract 99 from both sides of the equation. m+9−9=±92−9m + 9 - 9 = \pm\sqrt{92} - 9 m=±92−9m = \pm\sqrt{92} - 9
  6. Take square root: Calculate the approximate values of mm.m≈±9.60−9m \approx \pm9.60 - 9m≈9.60−9m \approx 9.60 - 9 or m≈−9.60−9m \approx -9.60 - 9m≈0.60m \approx 0.60 or m≈−18.60m \approx -18.60Round the non-terminating values to the nearest hundredth.

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