Question

Use the method of completing the square to solve the equation x^2-8x+1=0

to find the values of x.
Give your answer in the form a+-sqrt(b)

Answer 1

• a = 4
• b = 15

Explanation:

You want to solve x² -8x +1 = 0 using the method of completing the square.

Square of a binomial

We know that the square of a binomial is ...

(x -a)² = x² -2ax +a²

That is, the constant in the trinomial is the square of half the x-term coefficient: ((-2a)/2)² = a².

Application

In the given equation, the x-term coefficient is -8, so the constant in the perfect square trinomial will be ...

(-8/2)² = 16

The constant in the equation is already 1, so we need to add 15:

x² -8x +1 +15 = 15 . . . . . . . . add 15 to both sides

(x -4)² = 15 . . . . . . . . . . . write as a square

x -4 = ±√15 . . . . . . . . take the square root

x = 4 ±√15 . . . . . . add 4

Comparing this to the form a±√b, we see ...

• a = 4
• b = 15