Here are four equations, followed by worked solutions of the equations. Each solution has at least one error.
Solve one or more of these equations by completing the square.
Then, look at the worked solution of the same equation as the one you solved. Find and describe the error or errors in the worked solution.
Worked solutions (with errors):
1.
2.
3.
4.
13.3
Activity
Solve these equations by completing the square.
Student Lesson Summary
Completing the square can be a useful method for solving quadratic equations in cases in which it is not easy to rewrite an expression in factored form. For example, let’s solve this equation:
First, we’ll add to each side to make things easier on ourselves.
To complete the square, take of the coefficient of the linear term, 5, which is , and square it, which is . Add this to each side:
Notice that is equal to 25, and rewrite it:
Since the left side is now a perfect square, let’s rewrite it:
For this equation to be true, one of these equations must true:
To finish up, we can subtract from each side of the equal sign in each equation.
It takes some practice to become proficient at completing the square, but it makes it possible to solve many more equations than we could by methods we learned previously.
