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Solve for "x" by factoring

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5 Answers

2x(4x - 5) = 3; Solve for x by factoring.
  • First we have to convert the equation to 0 = ax2 + bx + c
  • Start by distributing 2x throughout the parentheses
2x(4x - 5) = 3
(2x)(4x) - (2x)(5) = 3
8x2 - 10x = 3
  • Then subtract 3 from both sides to make the equation equal 0
8x2 - 10x - 3 = 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
Product               Sum
-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
8x2 + 2x - 12x - 3 = 0
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 = 0
2x = 3
x = 3/2
 
4x + 1 = 0
4x = -1
x = -1/4
 
  • Finally, we should check our work.
x = 3/2
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
Hi Jack;
2x(4x-5)=3
Let's distribute the 2x...
8x2-10x=3
Let's subtract 3 from both sides...
8x2-10x-3=3-3
8x2-10x-3=0
For the FOIL...
FIRST must be (8x)(x) or (4x)(2x).
OUTER and INNER must add-up to -10x.
LAST must be (3)(1) or (1)(3) and one number must be negative to result in the product of -3.
(4x+1)(2x-3)0
Let's FOIL...
FIRST...(4x)(2x)=8x2
OUTER...(4x)(-3)=-12x
INNER...(1)(2x)=2x
LAST...(1)(-3)=-3
8x2-12x+2x-3=0
8x2-10x-3=0
(4x+1)(2x-3)=0
Either or both parenthetical equation(s) must equal zero...
4x+1=0, 4x=-1, x=-1/4
2x-3=0, 2x=3, x=3/2
2x(4x-5)=3
 
Expand by opening the brackets
 
8x2 - 10x = 3
 
Cross 3 over to the left to become -3 and the equation equals 0
 
8x2 - 10x - 3 = 0
 
Now finding the factors of the equation
 
8x2 - 12x + 2x - 3 = 0
 
(8x2 - 12x) + (2x - 3) = 0
 
4x(2x - 3) + 1(2x - 3) = 0
 
(4x + 1)(2x - 3) = 0
 
(4x + 1) = 0
 
4x + 1 = 0
 
4x = -1
 
x = -1/4
 
or
 
(2x - 3) = 0
 
2x - 3 = 0
 
2x = 3
 
x = 3/2

 

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