Question

Solve for xX² + 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