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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinet2−20t+____t^2 - 20t + \_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinet2−20t+____t^2 - 20t + \_\_\_\_
  1. Identify Coefficients: Identify the coefficients of the polynomial t2−20t+_t^2 - 20t + \_ to compare with the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1 (coefficient of t2t^2)
    b=−20b = -20 (coefficient of tt)
    c=?c = ? (the number we need to find)
  2. Calculate Completing Square Value: To complete the square, we need to add (b2)2(\frac{b}{2})^2 to the polynomial. In this case, b=−20b = -20. Calculate (−20/2)2(-20/2)^2 to find the value that completes the square. (−20/2)2=(−10)2=100(-20/2)^2 = (-10)^2 = 100
  3. Complete the Square: The number that completes the square for the polynomial t2−20t+_(_t^2 - 20t + \_\\(\_\\_\) is 100100. So, the polynomial becomes a perfect-square quadratic: t2−20t+100t^2 - 20t + 100.

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