Question

How do you solve using the completing the square method `2x^2 + 6x -5 =0`?

Answer 1

`x=-3/2+-1/2sqrt19`

Explanation:

`"using the method of "color(blue)"completing the square"`

`• " the coefficient of the "x^2" term must be 1"`

`"factor out "2`

`rArr2(x^2+3x-5/2)=0`

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2+3x`

`rArr2(x^2+2(3/2)xcolor(red)(+9/4)color(red)(-9/4)-5/2)=0`

`rArr2(x+3/2)^2+2(-9/4-5/2)=0`

`rArr2(x+3/2)^2-19/2=0`

`rArr2(x+3/2)^2=19/2`

`rArr(x+3/2)^2=19/4`

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

`sqrt((x+3/2)^2)=+-sqrt(19/4)larrcolor(blue)"note plus or minus"`

`rArrx+3/2=+-1/2sqrt19`

`rArrx=-3/2+-1/2sqrt19larrcolor(red)"exact solutions"`