2x(4x-5)=3
2x(4x - 5) = 3; Solve for x by factoring.
- First we have to convert the equation to 0 = ax^{2} + bx + c
- Start by distributing 2x throughout the parentheses
(2x)(4x) - (2x)(5) = 3
8x^{2} - 10x = 3
- Then subtract 3 from both sides to make the equation equal 0
- Now we can factor
- To do this we must find two numbers whose product is equal to 8 times -3 and whose sum is equal to -10
- (8)(-3) = -24
-1 · 24 = -24 -1 + 24 = 23 (no)
-2 · 12 = -24 -2 + 12 = 10 (close!)
2 · -12 = -24 2 - 12 = -10 (Yes!)
- Next we need to rewrite the equation with the b term split into our two factors
- If our first try doesn't work we have to switch the two numbers
2x(4x + 1) - 3(4x + 1) = 0^{
}
(2x - 3)(4x + 1) = 0
- It worked!
- Now we need to solve for both values of x that will make the equation equal 0
2x = 3
x = 3/2
4x + 1 = 0
4x = -1
x = -1/4
- Finally, we should check our work.
2x(4x - 5) = 3
2(3/2)(4(3/2) - 5) = 3
(6/2)(12/2 - 5) = 3
3(6 - 5) = 3
3(1) = 3
3 = 3 √
x = -1/4
2x(4x - 5) = 3
2(-1/4)(4(-1/4) - 5) = 3
(-2/4)(-4/4 - 5) = 3
-1/2(-1 - 5) = 3
-1/2(-6) = 3
6/2 = 3
3 = 3 √
x = 3/2 and -1/4