Quadratic Equation Example Using Completing the Square Method

Find the roots of the equation y=m²+7m+10 by using completing the square method, and factorise it.

At this stage we set y = 0, and move the c coefficient to the RHS.

Find half of the b coefficient.

Square the answer from the previous step.

Add it to both sides of the equation. By adding it to both sides, the equation remains balanced.

We can now complete the square on the LHS as shown above.

Eliminate the square term, by taking the square root on both sides.

As you can see, now it is just a simple matter of solving for m.

Finally, these are the roots.

We can now use the roots to factorise.