Fill in the blank with a number to make the expression a perfect square.

Ask by Graham Griffin. in the United States

Mar 25,2025

Question

Fill in the blank with a number to make the expression a perfect square. $$ \left.u^{2}-14 u+\square\right] $$

UpStudy AI · Accepted Answer

1. Write the quadratic expression:
   $$
   u^2 - 14u + \square
   $$

2. To complete the square for an expression in the form 
   $$
   u^2 - 2au + a^2,
   $$
   we need to determine $$a$$ such that:
   $$
   -2a = -14.
   $$
   Solve for $$ a $$:
   $$
   a = \frac{14}{2} = 7.
   $$

3. Therefore, the constant term that makes the expression a perfect square is:
   $$
   a^2 = 7^2 = 49.
   $$

4. The perfect square expression is:
   $$
   u^2 - 14u + 49 = (u - 7)^2.
   $$

The missing number is $$ 49 $$.
The missing number is 49.

Fill in the blank with a number to make the expression a perfect square.

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