How would i solve this equation by factoring ?

Question

5x^2 + 9x - 72 =0

The solution would be what x =?

Answer 1

(ax+b)(cx+d)=0 is the format of a factored quadratic.

 

After "FOIL"ing that expression, you have

 

(a•c)x^2+(a•d+b•c)x+(b•d)=0 

 

5     x^2 +     9       x    -72 =0

 

Using your equation,

a•c=5, so  a=1 and c=5, or a=5 and c=1

b•d=-72, so b={1,2,3,4,6,8,9,12,18,24,36,72} and d=negative{72,36,24,18,12,9,8,6,4,3,2,1}

a•d+b•c=9, so you search for the right combination of those numbers.

 

The positive value of a•d or b•c will be greater, as 9 is positive. 

 

So I look for a 5•d +(1•c) when d is positive.  I could not find any: 5•8 +1•-9=40+-9=31

                                                                                                5•6+1•-12=30+-12=18.

                                                                                                5•4 +1•-18=20+-18=2

 

Then I look for 5•d +(1•c) when d is negative.  5•-3=-15, 1•24= 9

 

So I find the answer

 

(5x+24)(x-3)=5x^2 -15x +24x -72 =0

 

So now, use both binomials to solve what values of x would give you a 0 in that equation.

 

 

 

X

Answer 2

A fun way to remember the quadratic formula is to sing it to the tune of pop goes the weasel:

 

x equals negative b

Plus or minus the square root (of)

b squared minus four a c

All divided by two a

 

The "all" is where you would sing "pop" in the song.  It's saved me a lot of times, hope it helps you.

Answer 3

Hi Harry,

 

To solve this equation we will need to use the following Quadratic formula:

 

For ax² + bx + c = 0, the value of x is given by

 

x = -b ± √(b² - 4ac)

             2a

 

Therefore for the equation 5x² + 9x -72 = 0, if a=5, b=9 and c=-72, our quadratic equation will be:

x = -9 ± √(9² - 4(5)(-72))

              2(5)

 

= -9 ± √(81 - 4(-360))

            10

 

= -9 ± √(81 + 1440)

           10

 

= -9 ± √1521   => x = -9 + 39  OR x = -9 - 39

        10                           10                    10

 

==> x = 3 OR x = -4.8

 

Hope this helps and let me know if you have any other questions!

 

 

Answer 4

The easiest way to factor is to see right away that x=3 is a solution.

 

5*3²+9*3-72=0 ⇔ 45+27-72=0 ⇔0=0 --identity.

 

Then you need to search for another solution by considering that 5x²+9x-72=(x-3)(5x-a) and figure which x₂ would work. You can immediately see that 3a=-72 or a=-24; 

 

So 5x²+9x-72=(x-3)(5x+24), so

x₁=3

x₂=-24/5;

Answer 5

For factoring start out with (  ) (  ) double brackets

 

factor the first term 5x^2 (which is 5x & 1x place them as indicated below)

(5x     )(x    )

 

Now think of factor of -72  For example (8 & 9 , 12 & 6, 1 & 72, 18 & 4 36 & 2, 3 & 24, etc each with opposite sign since we need -72) but now you also have 5 to take account to get the middle term  9x

 

(5x +9)(x-8) Double check your work by FOIL method: 5x^2 -40x+9x-72 = 5x^2 -31x-72, does not work

 

so place each factor and keep trying until you have 9x as the middle term.

 

After trying most of the above

 

(5x+24) (x-3)  Double check: 5x^2 -15x+24x-72 = 5x^2 + 9x - 72. It works so now solve for x

 

(5x+24) (x-3) = 0  

 

5x+24 = 0      &    x-3 = 0

5x = -24         &    x= 3

 

x= -24/5        &      x= 3   answer