Question

Using the completing the square method, which of the following is the solution to x2 + 4x - 7 = 0?

A.x = -2 - √11, x = -2 + √11


B.x = 2 - √3, x = 2 + √3


C.x = 2 - √11, x = 2 + √11


D.x = -2 - √3, x = -2 + √3

Answer 1

We are completing the square for


`x^2+4x-7=0`

Add +7 to both sides

`x^2+4x=7`

Next add


`((4)/(3))^2`
to both side

Notice that the Left hand side is a perfect square. That is


`(x+2)^2= 7+4`


`(x+2)^2= 11`
Take square root of both sides


`(x+2)= \mp \sqrt(11)`

`x= -2 \mp \sqrt(11)`


`x= -2 - \sqrt(11)\: or \:x= -2 - \sqrt(11)`

`<B>The correct answer is A</B>`