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## How would i solve this equation by factoring ?

5x^2 + 9x - 72 =0
The solution would be what x =?

(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

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

(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
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.
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!

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;
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