slove the equation

Question

x^2+5x-40=0

Answer 1

First, we'll try this by factoring.....

 

First, note the negative 3rd term.  This means the factors will be in the form (x + A)(x -B).  since the middle term is positive, then A must be larger.

 

So A - B = 5

and

A times B = -40

 

factor 40 = 2*2*2*5

by inspection, there is no integer solution---so lets use the quadratic formula:

 

For ax^2 + bx + c, the value of x is:   (-b ± √(b^2 - 4ac)) / 2a

 

Plug in the numbers using the original equation:

 

x = (-5 ± √(25 + 160)) / 2

x = (-5 ± √185 ) / 2

x = (-5 ± 13.6 ) / 2

 

x = -9.3 , +4.3

 

CHECK:

(-9.3)^2 + 5(-9.3) -40 = ?

86.5 - 46.5 -40 = 0

 

(-4.3)^2 + 5(4.3) -40 = ?

18.5 - 21.5 - 40 = 0

 

Answer 2

Hi Natalie,

Quadratic equation ax² + bx + c=0, then

 

                             x = -b ±√b²  -4ac / 2a

 

 for eqn x² +5x-40=0  , a=1, b=5 c=-40

 using this formula, 

 

x = -5 ±√5² -4(-40) /2(1)

    

    =-5 ±√185  /2