Question

Express x^2-8x+5 in the form (x-a)^2-b where a and b are intergers

Answer 1

(x - 4)² - 11

Explanation:

x² - 8x + 5

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

x² + 2(- 4)x + 16 - 16 + 5

= (x - 4)² - 11

Answer 2

(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