Answer:
(x - 4)^2 - 11
Explanation:
Here, the question asks you to complete the square. The steps to do so are the following:
ax^2 + bx + c = a(x - b/2 x)^2 -(b/2)^2 + c
1. halve the x coefficient and put it with x as a binomial squared
2. minus the new coefficient squared
3. collect like terms
so let's do it for this question:
x^2 - 8x + 5
step 1:
half of -8, is -4, so we'll get:
= (x - 4)^2 + 5
However this isn't equal to x^2 - 8x + 5, but to x^2 - 8x + 16 + 5. Therefore we must get rid of 16 (step 2). You will notice 16 = (-4)^2 (from the first formula I gave.)
= (x - 4)^2 - 16 + 5
step 3:
= (x - 4)^2 - 11