2x^2 + 7x - 9 = 0

Question

all real solutions

Answer 1

Once you can accomplish arranging to get ax²+bx +c = 0...

 

you can use the Quadratic Equation:  [-b +/- sqrt(b² - 4ac)] / (2a) to solve for x

 

= [-7 +/- sqrt[49 - 4(2)(-9)] / (2(2)

 

= [-7 +/- sqrt[49-(-72)] / 4

 

= [-7 +/- sqrt(121)]/ 4

 

= -7/4 +/- 11/4

 

x = 1 and x = -9/2

Answer 2

 A general rule is:

 

 

    2 X² + 7X - 9 = 0                 to find 2 numbers whose sum is +7, and their product is -18 .

                                                  those numbers are    +9 , - 2

     2X² - 2X + 9X - 9 =0                break up 7X  into 9X , - 2X .

 

     2X ( X - 1) + 9 ( X - 1 ) =0            factoring by grouping .

 

      ( X - 1 ) ( 2X + 9 ) = 0

 

       X - 1 = 0     X = 1

 

      2X + 9 = 0       X = - 9/2       

                                                        

Answer 3

This factors as

 

(x-1)(2x +9) = 0

 

So the solutions are  x = 1     and  x = -9/2