Question

Solve the equation by completing the square.

x² + 4x = 12

Answer 1

the first thing to do in completing the square is to change ax^2 + bx + c = 0 into ax^2 + bx = -c which seems to be done since the constant (12) is already on the right hand side. Now, we must solve for the third term of the Left Hand Side. to get it,first we divide the middle term by 2...

4/2 = 2

now we square it

2^2 = 4

we add 4 to the LHS now. BUt since we added 4 to the LHS we add 4 to the RHS too so we have...

x^2 + 4x + 4 = 12 + 4

x^2 + 4x + 4 = 16

the LHS is a perfect square trinomial so we can factor it out into

(x+2)^2 = 16

we square root....

x+ 2 = +/- 4

x = 4 - 2 and x = - 4-2

so...

x = 2
x = -6