Solve equations by factorising and completing the square
We addressed this point in year 8, year 9 and year 10. We will now review on factorising and completing the square.
Example 1. - factorising
In this example, the equation can be factorised to get: x(x - 4) = 0.
Therefore x = 0 or x = 4.
Therefore x = 0 or x = 4.
Example 2. - completing the square
In this example we will use the "completing the square" method. Move the 10 to the right side to get: x^2 - 8x = - 10. Then, halve the -8 to get - 4, which then needs to be squared and added to both sides to get: x^2 - 8x + 16 = -10 + 16.
Therefore (x - 4)^2 = 6
x - 4 = root 6 or x - 4 = - root 6
Therefore x = root 6 + 4 or x = 4 - root 6
Therefore (x - 4)^2 = 6
x - 4 = root 6 or x - 4 = - root 6
Therefore x = root 6 + 4 or x = 4 - root 6