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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlines2−16s+____s^2 - 16s + \_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlines2−16s+____s^2 - 16s + \_\_\_\_
  1. Identify coefficients: Identify the values of aa, bb, and cc in the polynomial s2−16s+?s^2 - 16s + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.a=1a = 1b=−16b = -16c=?c = ?
  2. Calculate half value: To complete the square, we need to add the square of half of the coefficient of ss, which is b2\frac{b}{2}, to the polynomial.\newlineHalf of −16-16 is −162-\frac{16}{2}, which equals −8-8.
  3. Square half value: Now, square the value obtained in the previous step to find the number that completes the square.\newline(−8)2(-8)^2 equals 6464.
  4. Complete the square: The number that completes the square is 6464. So the polynomial becomes a perfect-square quadratic when we add 6464 to it.\newlineThe completed square form is s2−16s+64s^2 - 16s + 64.

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