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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineh2+12h+____h^2 + 12h + \_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineh2+12h+____h^2 + 12h + \_\_\_\_
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic expression h2+12h+?h^2 + 12h + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.a=1a = 1b=12b = 12c=?c = ?
  2. Calculate value: To complete the square, we need to add (b2)2(\frac{b}{2})^2 to the expression h2+12hh^2 + 12h. Calculate (122)2(\frac{12}{2})^2.\newline(122)2=(6)2=36(\frac{12}{2})^2 = (6)^2 = 36
  3. Add to expression: Add the calculated value to the expression to make it a perfect-square quadratic: h2+12h+36h^2 + 12h + 36. Check if (h+6)2(h + 6)^2 equals h2+12h+36h^2 + 12h + 36. (h+6)2=h2+2∗(h∗6)+62=h2+12h+36(h + 6)^2 = h^2 + 2*(h*6) + 6^2 = h^2 + 12h + 36

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