Question

How do you solve `x²+6x+2=9`?

Answer 1

`x = 1 or x = -7`

Explanation:

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

Collecting like terms;

`x^2 + 6x +2 - 9 = 0`

`x^2 + 6x - 7 = 0`

Using Factorization Method..

Factors: `1 and 7`

`6x = 7x - 1x`

`-7 = 7 xx -1`

Therefore;

`x^2 - x + 7x - 7 = 0`

Grouping;

`(x^2 -x)+(7x - 7) = 0`

Factorizing;

`x(x - 1) +7(x - 1) = 0`

`(x - 1) (x + 7) = 0`

`x - 1 or x + 7 = 0`

`x = 1 or x = -7`

Answer 2

`x=1` and `x=-7`

Explanation:

We're dealing with a quadratic, so we want to set it equal to zero to find its zeroes. We now have

`x^2+6x-7=0`

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

What two numbers sum up to `6` and have a product of `-7`? After some trial and error, we arrive at `-1` and `7`. Now, we can factor this as

`(x-1)(x+7)=0`

Setting both factors equal to zero, we get

`x=1` and `x=-7`

Hope this helps!