Complete
$(x+\square)^2=$
Answer (2)
Assume the missing term is 'a'.
Expand the expression ( x + a ) 2 to get x 2 + 2 a x + a 2 .
Express the completed square in general form: ( x + a ) 2 = x 2 + 2 a x + a 2 .
The completed expression is ( x + a ) 2 = x 2 + 2 a x + a 2 .
Explanation
Understanding the Problem We are given an incomplete expression ( x + □ ) 2 and asked to complete it. This means we need to find what goes in the square. Let's call the missing term 'a'.
Expanding the Expression So we have ( x + a ) 2 . Expanding this gives us x 2 + 2 a x + a 2 . Since the problem is incomplete, we cannot determine a specific numerical value for 'a'. We need more information, such as the coefficient of the x term or the constant term after expansion.
General Form of Completed Square Without additional information, we can only express the completed square in general form: ( x + a ) 2 = x 2 + 2 a x + a 2 .
Final Answer Since we cannot determine a specific value for the missing term, we will express the answer in terms of a variable 'a'. Therefore, the completed expression is ( x + a ) 2 = x 2 + 2 a x + a 2 .
Examples
Completing the square is a technique used in algebra to convert a quadratic expression into a perfect square trinomial. For example, if you're trying to solve a quadratic equation like x 2 + 6 x + 5 = 0 , completing the square helps rewrite it in the form ( x + a ) 2 + b = 0 , making it easier to find the solutions for x . This method is also used in various fields like physics to solve problems involving projectile motion or optimization problems in engineering to design efficient systems.
To complete the expression (x+ox)^2 , we denote the missing term as 'a' and expand to get ( x + a ) 2 = x 2 + 2 a x + a 2 . This generalized expression allows us to represent our solution without specific values for 'a'.
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