Question

How do you solve using the completing the square method `2x^2 - 7x - 15 = 0`?

Answer 1

`x=-3/2" or "x=5`

Explanation:

`"to use the method of "color(blue)"completing the square"`

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

`rArr2(x^2-7/2x-15/2)=0`

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2-7/2x`

`2(x^2+2(-7/4)xcolor(red)(+49/16)color(red)(-49/16)-15/2)=0`

`rArr2(x-7/4)^2+2(-49/16-15/2)=0`

`rArr2(x-7/4)^2-169/8=0`

`rArr2(x-7/4)^2=169/8`

`rArr(x-7/4)^2=169/16`

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

`rArrx-7/4=+-sqrt(169/16)larrcolor(blue)"note plus or minus"`

`rArrx=7/4+-13/4`

`rArrx=7/4-13/4=-3/2" or "x=7/4+13/4=5`