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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinem2+6m+____m^2 + 6m + \_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinem2+6m+____m^2 + 6m + \_\_\_\_
  1. Identify values: Identify the values of aa, bb, and cc in the polynomial m2+6m+?m^2 + 6m + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1
    b=6b = 6
    c=?c = ?
  2. Complete the square: To complete the square for the polynomial m2+6mm^2 + 6m, we need to add (b/2)2(b/2)^2 to it.\newlineCalculate (b/2)2(b/2)^2 using b=6b = 6.\newline(b/2)2=(6/2)2(b/2)^2 = (6/2)^2
  3. Simplify expression: Simplify the expression (62)2(\frac{6}{2})^2 to find the missing number in m2+6m+____m^2 + 6m + \_\_\_\_.(62)2=(3)2=9\left(\frac{6}{2}\right)^2 = (3)^2 = 9The missing number is 99.

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