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2x^2 + 7x - 9 = 0

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3 Answers

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
 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       
                                                        

Comments

Students should be encouraged to factor the quadratic first. Because it is important later on, when dealing with differential equations, and solutions of higher degree equations to be able to determine the conditions in which the solutions are rational/ irrational or complex. 

Comment

This factors as
 
(x-1)(2x +9) = 0
 
So the solutions are  x = 1     and  x = -9/2