SOLUTION: How do you solve 3x<sup>2</sup> - 5x = 8?

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Question 73947: How do you solve 3x2 - 5x = 8?
Found 3 solutions by stanbon, Earlsdon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
solve 3xto the second power -5x=8
3x^2-5x-8=0
Use the AC Method to factor:
3x^2-8x+3x-8=0
x(3x-8)+(3x-8)=0
(3x-8)(x+1)=0
Set each factor equal to 0 an solve for x:
x=8/3 or x=-1
===================
Cheers,
Stan H.
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Solve for x:
First, subtract 8 from both sides of the equation.
Now factor this trinomial.
Apply the zero product principle.
and/or
Add 8 to both sides.
Divide both sides by 3.
or This is one of the roots.
Subtract 1 from both sides.
This is the other root.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
how do you solve 3x2 - 5x = 8? 

3x² - 5x = 8

This is a quadratic equation. 

1. Get zero on the right by adding -8 to both sides

3x² - 5x - 8 = 0

2. Ignore the signs and multiply the 3 by the 8, getting 24

Think of two whole numbers whose product in 15 and whose

DIFFERENCE is 5. (DIFFERENCE because of the sign before the
 8 is - . If it had been + I would have said "SUM")

A little thinking gives us 8 and 3, because

8×3 = 24 and 8-3 = 5

Rewrite the 5 as (8-3)

3x² - (8-3)x - 8 = 0

Remove the parentheses

3x² - 8x + 3x - 5 = 0

Factor x out of the first two terms

x(3x - 8) + 3x - 5 = 0

Factor 1 out of the last two terms:
(Note: if you can't factor anything else 
out of one of the pair of terms, factor 
out 1 or -1.)

x(3x - 8) + 1(3x - 8) = 0

Now I'll do some coloring to help
you see what I'm doing:

x(3x - 8) + 1(3x - 8) = 0

Now factor out the red (3x - 8),
putting the blue x and the blue + 1 inside parentheses

(3x - 8)(x + 1) = 0

Set each factor = 0 and solve for x

3x - 8 = 0           x + 1 = 0
    3x = 8               x = -1
     x = 8/3

Edwin

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