Question

What are the values of x in the equation x2 - 6x + 9 = 25?x = -2 or x = 8x= -1 or x = -11x= 1 or x = 11x = 2 or x = -8

Answer 1

Given the equation:

`x^2\text{ - 6x + 9 = 25}`

First, let the equation equals zero by moving 25 to the left hand side:

`\begin{gathered} x^2\text{ - 6x + 9 -25 = 0} \\ x^2\text{ - 6x -16}=\text{ 0} \end{gathered}`

now factorize the equation:

`*^2\text{ - 6x - 16}=\text{ 0}`
`*^2\text{ - 8x + 2x - 16 = 0}`
`*(x\text{ -8) + 2(x - 8) = 0}`
`(x\text{ + 2)(x - 8) = 0}`

Therefore

x + 2 = 0;