SOLUTION: Solve equation by using factoring without using the quadratic formula. 4x(3x+7)=5

Algebra.Com
Question 888536: Solve equation by using factoring without using the quadratic formula.
4x(3x+7)=5
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
12x^2+28x-5=0
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .



Now multiply the first coefficient by the last term to get .



Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?



To find these two numbers, we need to list all of the factors of (the previous product).



Factors of :

1,2,3,4,5,6,10,12,15,20,30,60

-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to .

1*(-60) = -60
2*(-30) = -60
3*(-20) = -60
4*(-15) = -60
5*(-12) = -60
6*(-10) = -60
(-1)*(60) = -60
(-2)*(30) = -60
(-3)*(20) = -60
(-4)*(15) = -60
(-5)*(12) = -60
(-6)*(10) = -60


Now let's add up each pair of factors to see if one pair adds to the middle coefficient :



First NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+10=4




From the table, we can see that the two numbers and add to (the middle coefficient).



So the two numbers and both multiply to and add to



Now replace the middle term with . Remember, and add to . So this shows us that .



Replace the second term with .



Group the terms into two pairs.



Factor out the GCF from the first group.



Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.



Combine like terms. Or factor out the common term



===============================================================



Answer:



So factors to .



In other words, .



Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
RELATED QUESTIONS

Using the quadratic equation x^2 - 4x - 5 = 0, perform the following tasks: Solve by... (answered by ikdeep)
using the quadratic equation x² - 4x - 5 = 0, perform the following task: solve by... (answered by AnlytcPhil)
1) Solve the quadratic equations by factoring: 5x² = 125 2) Solve the quadratic... (answered by checkley71)
1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve (answered by mukhopadhyay)
Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by... (answered by fractalier)
1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve (answered by josmiceli)
Solve by using the quadratic formula. 5x2 + 3x =... (answered by Earlsdon)
Please Help Me!!! Solve equation by using the quadratic formula... (answered by vleith)
1) Using the quadratic equation x2 – 4x – 5 = 0, perform the following tasks: a) Solve (answered by checkley75)