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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineh2−6h+____h^2 - 6h + \_\_\_\_

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Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineh2−6h+____h^2 - 6h + \_\_\_\_
  1. Identify coefficients and compare: Identify the coefficients of the polynomial h2−6h+?h^2 - 6h + ? and compare it with the standard quadratic form ax2+bx+cax^2 + bx + c. Here, a=1a = 1 and b=−6b = -6. We need to find the value of cc that makes the polynomial a perfect square.
  2. Calculate half and square: To complete the square, we take half of the coefficient of hh, which is −6-6, and then square it.\newlineHalf of −6-6 is −3-3, so we square −3-3 to get 99.
  3. Complete the square: The number that completes the square is 99. Therefore, the polynomial becomes a perfect-square quadratic when we add 99 to it.\newlineThe completed square form is h2−6h+9h^2 - 6h + 9.

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