x^2+4x=10 how do you solve this by completing the square?

Question

I don't understand completing the square.

 

Answer 1

Given equation x^2+4x = 10

To complete the squre add 4 to each side.

x^2+4x+4 = 10+4

(x+2)^2 = 14

Apply squre root on each side.

√(x+2)^2 = √14

x+2 = √14

Subtract 2 from each side.

x+2-2 = √14 -2

x = √14 -2

Solution x = √14 -2.

Comments

The solution of the equation is x = - 2 + √14 and x = - 2 - √14.

Answer 2

The equation is x² + 4x = 10.

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 4. so, (half the x coefficient)² = (4/2)²= 4.

Add 4 to each side.

x² + 4x + 4 = 10 + 4

(x + 2)² = 14

(x + 2)² = (± √14)²

x + 2 = ± √14

x = - 2 + √14 and x = - 2 - √14.

The solutions are x = - 2 + √14 and x = - 2 - √14.