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Solve by completing the square.\newlinem2+12m−23=0m^2 + 12m - 23 = 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+12m−23=0m^2 + 12m - 23 = 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. Move Constant Term: Start with the equation m2+12m−23=0m^2 + 12m - 23 = 0. We want to complete the square for the left side of the equation. First, move the constant term to the right side by adding 2323 to both sides. m2+12m=23m^2 + 12m = 23
  2. Complete the Square: To complete the square, we need to add (122)2(\frac{12}{2})^2 to both sides of the equation.\newline(122)2=62=36(\frac{12}{2})^2 = 6^2 = 36\newlineSo we add 3636 to both sides:\newlinem2+12m+36=23+36m^2 + 12m + 36 = 23 + 36\newlinem2+12m+36=59m^2 + 12m + 36 = 59
  3. Factor Perfect Square Trinomial: Now, factor the left side of the equation which is a perfect square trinomial. \newline(m+6)2=59(m + 6)^2 = 59
  4. Take Square Root: Take the square root of both sides of the equation to solve for mm.(m+6)2=±59\sqrt{(m + 6)^2} = \pm\sqrt{59}m+6=±59m + 6 = \pm\sqrt{59}
  5. Isolate Variable: Isolate mm by subtracting 66 from both sides of the equation.\newlinem=−6±59m = -6 \pm \sqrt{59}
  6. Calculate Approximate Values: Calculate the approximate decimal values of mm by taking the square root of 5959 and rounding to the nearest hundredth.59≈7.68\sqrt{59} \approx 7.68So we have:m≈−6+7.68m \approx -6 + 7.68 or m≈−6−7.68m \approx -6 - 7.68m≈1.68m \approx 1.68 or m≈−13.68m \approx -13.68

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