Question

Solve for x
X² + 2x-5=0​

Answer 1

To solve this, we have to complete the square of
`x^(2) +2x`

To do this with halve the
`2x` and get rid of the x, then get rid of the power on
`x^(2)`, and then put them all in brackets, and the square the bracket, like so:

`x^(2) +2x` becomes
`(x+1)^(2)`

However
`(x+1)^(2)` does not equal
`x^(2) +2x`

If we expand
`(x+1)^(2)` we get
`x^(2) +2x + 1` instead.

So to make it equal, all we do is subtract 1.

So when we complete the square of
`x^(2) +2x` , we get
`(x+1)^(2)-1`

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So
`x^(2) +2x - 5=0` becomes:

`(x+1)^(2)-1-5=0`

`(x+1)^(2)-6=0`

`(x+1)^(2)=6`

x + 1 = ±√6

x = -1 ± √6

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Answer:

x = -1 ± √6