For the equation : x^2+2x=4 find the exact roots.

If you move the 4 over, x^2+2x-4=0, you get a quadratic that does not factor. So, you have two choices here. Use the quadratic formula or complete the square.

Quadratic formula: x = (-b +- sqrt(b^2 - 4ac))/(2a) Here, a=1, b=2, c=-4.

x= (-2 +- sqrt(4-4(1)(-4))/(2*1) = (-2 +- sqrt(20))/(2) now sqrt(20) = sqrt(4)*sqrt(5) =2 * sqrt(5)

so, x = (-2 +- 2*sqrt(5))/2 now factor out a 2: 2(-1 +- sqrt(5))/2 then cancel the 2's

x = -1 +- sqrt(5)

Completing the square: x^2 + 2x = 4 half of 2 is one, square one and you get one, that is what you add to both sides: x^2 + 2x + 1 = 4 + 1

(x + 1)^2 = 5

x + 1 = +- sqrt(5)

x = -1 +- sqrt(5)

And there's your answers.