Below is a question from the Edexcel Maths Core 1 textbook, Solve the equation x^2 + 8x + 10 = 0 using completing the square.

Before we get to solving the equation, let’s first review the method completing the square.

Completing the square is simply to convert an equation into the form of (x±a )^2, so it is possible to solve for x.

Remember how you would open the bracket?

(x±a)^2=x^2±2ax+a^2

Completing the square is simply to go from the expanded form back to the square form (from left hand side to back to the right hand side).

Now, let’s look at the question. x^2 + 8x + 10 = 0

it looks similar to the expanded form (but it's not!) because if we assume the second item is 2ax, then 2ax = 8x, Divide both side by 2x, you get a = 4 (which squared equals to 16, not 10). So a^2=16 Now we know that we need a 16 in the equation to complete the square, which there is not one in the equation, so we need to add a 16 into the equation in order to complete the square, and subtract 16 from the equation at the same time so we still keep the weight of the right hand side, so the equation still balance.

x^2 + 8x +16 - 16 + 10 = 0 (x+4)^2-16+10=0 Tidy up the numbers together (x+4)^2-6=0 Move the -6 to the left-hand side (x+4)^2=6 Take the square root on both sides x+4=±√6 Move 4 to the other side x=±√6-4 Hence, the roots of x^2 + 8x + 10 = 0 are either x=√6-4 or x=-√6-4.