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Explain why the equation (x-4)2 - 28= 8 has two solutions. Then solve the equation to find the solutions. Show your work. 

 

 

 

 

 

This is Josh’s solution for the equation:

x2-6x-7=0

x2-6x=7

x2-6x+9=7+9

(x-3)2=16

x-3=16

x=19

x-3=-16

x= -13

       

Is Josh’s solution correct? Explain. 

Guest Mar 16, 2018
 #3
avatar+12565 
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(x-4)^2 -28 = 8     re-arrange to look like this

(x-4)^2 = 36    now take the square root

(x-4) = + or -  sqrt(36)        <-------- TWO answers

x-4 = 6   or  -6

x= 10  or  -2 

ElectricPavlov  Mar 16, 2018
edited by ElectricPavlov  Mar 16, 2018
 #4
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(x-4)^2 - 28= 8         add 28 to both sides

 

(x - 4)^2 =8+28

(x - 4)^2 = 36            take the square root of both sides

x - 4 = +or-6

x - 4 = 6                    add 4 to both sides

x = 10 - this is one solution

x - 4 = - 6                   add 4 to both sides

x = - 6 + 4

x = - 2 - this is the 2nd solution

It has 2 solution because it is a quadratic equation!.

Guest Mar 16, 2018
edited by Guest  Mar 16, 2018

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