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Solve each equation and express your answer in simplest radical form:

 

1.) 5x - 7x^2 = 3x + 4 

 

2.) -x^2 + 4x = 13

 Feb 27, 2019
 #1
avatar+17275 
+2

1.  5x - 7x^2 = 3x +4        add 7x^2 to both sides 0f the equation

     5x   =   7x^2 + 3x + 4      subtract 5x from both sides

      0 = 7x^2 -5x +3x+4        simplify

      0 = 7x^2 - 2x + 4          SInce the question states that it is 'radical form'   you will need to use Quadratic Formula (rather than factoring) to find 'roots'

      \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

 

a = 7    b = -2    c = 4   

    [ 2 +- sqrt((-2)^2 - 4(7)(4) ]   / [ 2(7) ]  = 2 +- sqrt(-108) / 14  =  2+- 6i sqrt(3)  / 14   =  1/7 +- 3/7 i sqrt(3)

 

Think you can do the second one now?

 

2.  - x^2 +4x = 13

         x^2 -4x +13 = 0         a = 1   b = -4   c = 13  

 Feb 27, 2019
edited by ElectricPavlov  Feb 27, 2019
edited by ElectricPavlov  Feb 27, 2019
edited by ElectricPavlov  Feb 27, 2019

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