PrerequisitesPrerequisite

Solving by completing the square - integer solutions

Complete the square, take both square roots and find two integer solutions.

  • Complete the square, keeping the equation balanced.
  • Isolate the squared parenthesis, then include both the positive and negative square roots.
  • Rearrange each branch to find the two values of .

Example 1

Solve by completing the square.

Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.Evaluate the plus and minus branches and list all solutions.

Example 2

Solve by completing the square.

Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.Evaluate the plus and minus branches and list all solutions.

Remember
If , then or . Remember both branches.

Your turn

Question 1

Solve by completing the square.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.Evaluate the plus and minus branches and list all solutions.
Question 2

Solve by completing the square.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.Evaluate the plus and minus branches and list all solutions.
Question 3

Solve by completing the square.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.Evaluate the plus and minus branches and list all solutions.
Question 4

Solve by completing the square.

Check answer
Halve to get ; subtract its square.Evaluate the plus and minus branches and list all solutions.
Question 5

Solve by completing the square.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.Evaluate the plus and minus branches and list all solutions.
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