Solve the problem.

Question

solve the problem.

 

 

 

5w^2 = 11w + 12

 

the solutions is w = ? ( Use a comma to separate the answers as needed)

Answer 1

-4, 3

 

5w^2 - 11w - 12 = 0

(5w _  ?)(w _ ?)

12 = 4x3 or 12x1

(5w + 4)(w - 3)

 

:)

 

 

Answer 2

1)First put the equation in the following form:

 

5w^2-11w-12=0

 

2)Now that the equation is set to zero we can factor the equation to find the roots.

 

This is probably the hardest part and it gets easier with practice.

 

The idea is to find two numbers that when multiplied together will give the right numbers in the original equation.

 

The basic formula is outer-outer=last, outer*outer + inner*inner = middle.  

 

By trial and error we can come up with the answer below.

 

(5w+4)(w-3)

 

This is the right factorization because the outer number -4 and 3 when multiplied equal -12. Along with this 5*1+-4*3=-11.

 

We can verify that this is the correct answer by multiplying the two factors to get the original equation

 

          5w+4

          w-3

          ------

         -15w-12

5w^2+4w

-----------------

5w^2-11w-12

 

3)Since the equation is set to zero each factor can be isolated to find each root individually. Zero divided by any number will equal zero. Therefore,

 

(w-3)(5w+4)=0

 

w-3 = 0 and 5w+4=0,

 

solving these two equations gives us the two roots

 

w=3 and w=-4/5.

 

The solution set is w={-4/5,3}

 

4) To verify this plug both roots back into the original equation

 

a)w=3

 

5*3^2=11*3+12

 

5*9=33+12

 

45=45

 

b)w=-4/5

 

a)5*(-4/5)^2=11*(-4/5)+12

 

16/5=-44/5+12

 

16/5=16/5

 

Answer 3

Hi Keith;

5w^2 = 11w + 12

Let's move everything to one side...

5w²-11w-12=0

For the FOIL...

FIRST must be (5w)(w)=5w²

OUTER and INNER must add-up to -11w

LAST must be (1)(12) or (12)(1) or (2)(6) or (6)(2) or (3)(4) or (4)(3) and one number must be negative to render the product of -12.

(5w+4)(w-3)=0

Let's FOIL...

FIRST...(5w)(w)=5w²

OUTER...(5w)(-3)=-15w

INNER...(4)(w)=4w

LAST...(4)(-3)=-12

5w²-15w+4w-12=0

5w²-11w-12=0

(5w+4)(w-3)=0

Either or both parenthetical equation(s) must equal zero...

5w+4=0..........w-3=0

5w=-4.............w=3

w=-4/5

 

Let's check our results...

5w^2 = 11w + 12...................5w^2 = 11w + 12

5(-4/5)²=[(11)(-4/5)]+12.......5(3)²=[(11)(3)]+12

5(16/25)=(-44/5)+12.............5(9)=33+12

16/5=(-44/5)+(60/5)..............45=45

16/5=16/5