Question

How do you factor `x^2+14x=-49`?

Answer 1

`(x+7)^2=0`

Explanation:

`x^2+14x=-49|+49`
`x^2+14x+49=0`

`"Complete the perfect square"`

`(x+14/2)^2+49-49=0`
`(x+7)^2=0`

Answer 2

`(x+7)^2`

Here's how I factored it:

Explanation:

`x^2 + 14x = -49`

To factor this, we first have to make one side equal to zero. We do this by adding `49` to both sides of the equation:
`x^2 + 14x + 49`

This is a perfect square trinomial:
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We know that:

• `14 = 2 xx 1 xx 7`
• `49 = 7 xx 7`

Therefore, the expression `x^2 + 14x + 49` is equivalent to:
`(x+7)^2`

`----------------`

To check our answer, let's see if `(x+7)^2` equals to the original expression:
`(x+7)(x+7)`
`x * x = x^2`

`x * 7 = 7x`

`7 * x = 7x`

`7 * 7 = 49`

And when we combine this we get:
`x^2 + 7x + 7x + 49`

We can still combine like terms (`7x + 7x`):
`x^2 + 14x + 49`

Therefore, we know that `(x+7)^2` is correct.

Hope this helps!