Question

How do you solve using the completing the square method `2x^2+8x-10=0`?

Answer 1

`x=-5`
`x=1`

Explanation:

`2x^2+8x-10=2[x^2+4x-5]`

`2[x^2+4x-5]=2[(x+2)^2-2^2-5]=2[(x+2)^2-9]=`

`2(x+2)^2-18=0`

`2(x+2)^2=18`

`(x+2)^2=9`

`x+2=+-3`

`x=+-3-2`

`x=-5`

`x=1`

Answer 2

`x=1` or `x=-5`

Explanation:

Divide both sides by `2` to get rid of the coefficient of `x^2`

`x^2+4x-5=0`

Add `5` to both sides

`x^2+4x=5`

Take half the coefficient of `x`, square it, and add to both sides

• The coefficient of `x` is `4`
• Half that is `2`
• The square of `2` is `4`
• Adding `4` to both sides gives

`x^2+4x+4=9`

Factoring the left hand side gives

`(x+2)^2=9`

The square root of both sides gives

`x+2=3` or `x+2=-3`
`x=1` or `x=-5`