How do you solve 8x^2 - 6x + 1 = 0 using the quadratic formula?

1 Answer
Jan 8, 2017

First, we "play with multipliers of 8 (1x8, 2x4, 4x2 8x1) and 1 to factor and then solve each term for 0:

8x^2 - 6x + 1 = 0

(4x - 1)(2x - 1) = 0

Now we solve each term of the factored quadratic for 0:

Solution 1)

4x - 1 = 0

4x - 1 + color(red)(1) = 0 + color(red)(1)

4x - 0 = 1

4x = 1

(4x)/color(red)(4) = 1/color(red)(4)

(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 1/4

x = 1/4

Solution 2)

2x - 1 = 0

2x - 1 + color(red)(1) = 0 + color(red)(1)

2x - 0 = 1

2x = 1

(2x)/color(red)(2) = 1/color(red)(2)

(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 1/2

x = 1/2