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Solve by completing the square.\newlinem2+12m=−13m^2 + 12m = -13\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+12m=−13m^2 + 12m = -13\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. Move Constant Term: Start with the equation m2+12m=−13m^2 + 12m = -13. To complete the square, we need to move the constant term to the right side of the equation. m2+12m+__=−13+__m^2 + 12m + \_\_ = -13 + \_\_
  2. Find Completing Number: Find the number to complete the square.\newlineThe coefficient of mm is 1212, so we take half of it, which is 66, and then square it to get 3636.\newlinem2+12m+36=−13+36m^2 + 12m + 36 = -13 + 36
  3. Add 3636: Add 3636 to both sides of the equation.\newlinem2+12m+36=23m^2 + 12m + 36 = 23\newlineNow the left side of the equation is a perfect square trinomial.
  4. Factor Left Side: Factor the left side of the equation.\newline(m+6)2=23(m + 6)^2 = 23
  5. Take Square Root: Take the square root of both sides of the equation.\newline(m+6)2=±23\sqrt{(m + 6)^2} = \pm\sqrt{23}\newlinem+6=±23m + 6 = \pm\sqrt{23}
  6. Solve for m: Solve for m by subtracting 66 from both sides.m=−6±23m = -6 \pm \sqrt{23}
  7. Calculate Approximate Values: Calculate the approximate decimal values of mm, rounding to the nearest hundredth.m≈−6+23m \approx -6 + \sqrt{23} and m≈−6−23m \approx -6 - \sqrt{23}m≈−6+4.80m \approx -6 + 4.80 and m≈−6−4.80m \approx -6 - 4.80m≈−1.20m \approx -1.20 and m≈−10.80m \approx -10.80

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