Question

How do you solve `10-2(x-1)^2=4`?

Answer 1

`x=1+-sqrt(3)`

Explanation:

This is in 'almost' completing the square format.

Subtract 10 from both sides

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

Lets make the LHS positive: Multiply both sides by (-1)

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

Divide both sides by 2

`(x-1)^2=3`

Square root both sides

`x-1=+-sqrt(3)`

Add 1 to both sides

`x=1+-sqrt(3)`

If you change this to decimals you will introduce rounding errors so leave it as it is.

Answer 2

`x=1 +- sqrt(3)`

Explanation:

Move 10 to the other side and divide by 2
`3 = (x-1)^2`
Take the square root.

Answer 3

`x=1+-sqrt3`

Explanation:

`"isolate "(x-1)^2`

`"subtract 10 to both sides"`

`cancel(10)cancel(-10)-2(x-1)^2=4-10`

`rArr-2(x-1)^2=-6`

`"divide both sides by "-2`

`cancel(-2)/cancel(-2)(x-1)^2=(-6)/(-2)`

`rArr(x-1)^2=3`

`color(blue)"take the square root of both sides"`

`sqrt((x-1)^2)=+-sqrt3larrcolor(blue)"note plus or minus"`

`rArrx-1=+-sqrt3`

`"add 1 to both sides"`

`rArrx=1+-sqrt3larrcolor(red)"exact solutions"`