Question

Solve x2 + 2x = 4 for x by completing the square.

Answer 1

x = √5 - 1, and x = - √5 - 1; Option B

Explanation:

See procedure below;

x^2 + 2x = 4,

( Write equation in form ) ⇒ x^2 + 2ax + a^2 = ( x + a )^2,

Solving for a; 2ax = 2x ⇒ a = 1,

x^2 + 2x + 1^2 = 4 + 1^2,

x^2 + 2x + 1^2 = 5,

( x + 1 )^2 = 5;

For f^2( x ) = a ⇒ solutions are √a, - √a,

x + 1 = √5, and x + 1 = - √5,

x = √5 - 1, and x = - √5 - 1;

Answer : x = √5 - 1, and x = - √5 - 1; Option B