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Algebra

How do you complete the square?

How do you complete the square? Learn the core idea, common steps, and how to recognize this algebra concept in homework problems.

Problem Statement

How do you complete the square?

Step-by-step solution

Problem Statement

How do you complete the square?

Step-by-Step Explanation

Completing the square rewrites a quadratic as a perfect square plus or minus a constant.

  1. Identify what the question is asking. In Algebra, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
  2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
  3. Work one step at a time and keep units, signs, and restrictions visible.
  4. Check whether the answer makes sense in the original context.

Key Formula

x2+bx=(x+b2)2−(b2)2x^2+bx=\left(x+\frac{b}{2}\right)^2-\left(\frac{b}{2}\right)^2

Final Answer

Completing the square rewrites a quadratic as a perfect square plus or minus a constant. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.