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:

x^{2}-6x-7=0

x^{2}-6x=7

x^{2}-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**+1 **

(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

#4**+1 **

(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