In the previous sections, you used the method of completing the square for expressions of the form x² + bx + c, where the coefficient of the x²-term was 1 as well as for where the coefficient of the x²-term was greater than 1. You may be wondering why you would ever need to complete the square.

In the interactive below, drag the tiles to the appropriate place in the figure to complete the chart. You may not need all of the tiles, or you may use some tiles more than once.

• How did you match the strategy with the situation?

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  Check Your Answer

  The equations from the situation column have been rewritten in the strategy column using the method of completing the square.

• How did you match the situation with the solution?

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  If the strategy was to solve a quadratic equation, the solution can be found using inverse operations. If the strategy was to rewrite an equation with both an x²-term and a y²-term, then the solution is the conic section represented by that equation.

Pause and Reflect

How does the method of completing the square help you to solve quadratic equations?

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Check Your Answer

Sometimes, a quadratic equation does not factor. When that is the case, completing the square allows you to write the quadratic equation as the square of a binomial, and you can use inverse operations to solve the equation.