How can I express x^2 - 7*x + 2 as (x - p)^2 + q ?

o One way to approach this question is to expand the right expression (x - p)² + q.
As we know from binomial expansions this gives us x² - 2px + p² + q.

o Now we need to ensure that we choose values for p and q such that the above expression is equal to x² - 7*x + 2. To find these values we can use the method of equating the coefficients which means that we look separately at the coefficients for x², x and the last part without x and equate these three parts in both terms.

o For x², the coefficients are luckily both times already 1, otherwise the example would not be solvable
o For x, the number 7 needs to be equal to 2p, hence p = 7/2
o For the term without x, 2 needs to be equal to (p² + q). p is already chosen to be 7/2, hence q = 2 - (7/2)² = 2 - 49/4 = -41/4 o This way we found that x² - 7x + 2 = (x - 7/2)² - 41/4