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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newliney2−14y+_____y^2 − 14y + \_\_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newliney2−14y+_____y^2 − 14y + \_\_\_\_\_
  1. Identify coefficients: Identify the values of aa, bb, and cc in the polynomial y2−14y+?y^2 − 14y + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1
    b=−14b = -14
    c=?c = ?
  2. Complete the square: Determine the value needed to complete the square. To complete the square of y2−14yy^2 - 14y, add (b/2)2(b/2)^2 to the polynomial.\newlineCalculate (b/2)2(b/2)^2 using b=−14b = -14.\newline(−14/2)2=(−7)2(-14/2)^2 = (-7)^2
  3. Find missing number: Simplify the calculation to find the missing number in y2−14y+_y^2 - 14y + \_.\newline(−7)2=49(-7)^2 = 49\newlineThe missing number is 4949.

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