The exact solutions to the quadratic equation 0 = 6x^{2} - 9x - 3 can be written in the form x=p+q√r. What is the value of p+q+r?

5 months ago

Some of the info you tried to copy didn't come through so I'm going to take a guess at what the question is. Feel free to ask again if I'm wrong!

0 = 6x^{2} - 9x - 3

0 = 3*(2x^{2} - 3x - 1)

This trinomial (2x^{2} - 3x - 1) cannot be factored further, so we use the quadratic equation.

This gives us the roots

x = 3/4 + sqrt(17/16)

x = 3/4 - sqrt(17/16)

If you don't want to use the quadratic formula, you can complete the square:

2x^{2} - 3x - 1 = 0 - divide by 2

x^{2 }- 3x/2 - 1/2 = 0 - add 1/2 to both sides

x^{2} - 3x/2 = 1/2

divide B (3/2) by two, square it, and add to both sides C = (3/2 * 1/2)^{2} = 9/16

Note, part of our root is going to be 3/2*1/2 =(3/4)

x^{2} - 3x/2 + 9/16 = 1/2 + 9/16

(x - 3/4)^{2} = 17/16

The square has a positive AND negative root ( sqrt(1) is both +1 and -1)

x - 3/4 = sqrt(17/16)

- (x - 3/4) = sqrt(17/16)

Solving for x, we get

Don't forget to put the two solutions back into your original equation to make sure both = 0!

5 months ago

## Answered By Emily D

Some of the info you tried to copy didn't come through so I'm going to take a guess at what the question is. Feel free to ask again if I'm wrong!

0 = 6x

^{2}- 9x - 30 = 3*(2x

^{2}- 3x - 1)This trinomial (2x

^{2}- 3x - 1) cannot be factored further, so we use the quadratic equation.This gives us the roots

x = 3/4 + sqrt(17/16)

x = 3/4 - sqrt(17/16)

5 months ago

## Answered By Emily D

If you don't want to use the quadratic formula, you can complete the square:

2x

^{2}- 3x - 1 = 0 - divide by 2x

^{2 }- 3x/2 - 1/2 = 0 - add 1/2 to both sidesx

^{2}- 3x/2 = 1/2divide B (3/2) by two, square it, and add to both sides C = (3/2 * 1/2)

^{2}= 9/16Note, part of our root is going to be 3/2*1/2 =(3/4)

x

^{2}- 3x/2 + 9/16 = 1/2 + 9/16(x - 3/4)

^{2}= 17/16The square has a positive AND negative root ( sqrt(1) is both +1 and -1)

x - 3/4 = sqrt(17/16)

- (x - 3/4) = sqrt(17/16)

Solving for x, we get

x = 3/4 + sqrt(17/16)

x = 3/4 - sqrt(17/16)

5 months ago

## Answered By Emily D

Don't forget to put the two solutions back into your original equation to make sure both = 0!