Question

How do you solve `x^2 - 6x + 9 = 25`?

Answer 1

`x=-2, 8`

Explanation:

Given quadratic equation:

`x^2-6x+9=25`

`x^2-6x-16=0`

`x^2-8x+2x-16=0`

`x(x-8)+2(x-8)=0`

`(x-8)(x+2)=0`

`x-8=0, x+2=0`

`x=8, x=-2`

`x=-2, 8`

Answer 2

`x=-2" or "x=8`

Explanation:

`"subtract 25 from both sides"`

`x^2-6x-16=0larrcolor(blue)"in standard form"`

`"the factors of "-16" which sum to "-6`
`"are "-8" and "+2`

`(x-8)(x+2)=0`

`"equate each factor to zero and solve for "x`

`x+2=0rArrx=-2`

`x-8=0rArrx=8`

Answer 3

`x=8` and `x=-2`

Explanation:

Since we have a quadratic, let's set it equal to zero to find its zeroes. This can be done by subtracting `25` from both sides.

We now have

`x^2-6x-16=0`

To factor this, let's do a little thought experiment:

What two numbers sum up to `-6` and have a product of `-16`? After some trial and error, we arrive at `-8` and `2`.

This means we can factor this as

`(x-8)(x+2)=0`

Setting both factors equal to zero, we get

`x=8` and `x=-2`

Hope this helps!

Answer 4

`x = 8" "` or `" "x = -2`

Explanation:

Given:

`x^2-6x+9=25`

Note that both the left hand side and the right hand side are perfect squares, namely:

`(x-3)^2 = 5^2`

Hence:

`x-3=+-5`

So:

`x = 3+-5`

That is:

`x = 8" "` or `" "x = -2`