Solve the equation by completing the square:x^2+7x= neg. 12?

Answer 1

Just to complete to previous answer, in case it isn't clear:

To make it a perfect square you add (-b/2a)^2 to both sides.
As noted:
(-7/2)^2 = 49/4

Starting with:
x^2 + 7x = -12

Add 49/4 to both sides:
x^2 + 7x + 49/4 = 49/4 - 12 = 1/4

Factor the perfect square:
(x + 7/2)^2 = 1/4

Now take the square root of both sides remembering that there are two roots (+ and -):
x + 7/2 = +/- 1/2

So there are two equations
x + 7/2 = 1/2 or x + 7/2 = -1/2

So x = -3 or x = -4

Answer 2

Completing the square basically means adding something to make the left side a perfect square. To do this, add (-b/2a)^2 to the left side where a is the coefficient of the quadratic term and b the coefficient of the linear term:
(-7/2)^2 = 49/4
x^2 + 7x + 49/4 = 49/4 - 12 = 1/4
(x + 7/2)^2 = 1/4

You can probably take it from there.

Answer 3

x^2 + 7x = -12

find half of 7, square it, add to both sides

x^2 + 7x + (49/4) = -12 + (49/4)
x^2 + 7x + (49/4) = (1/4)
factor left side into a perfect square
(x + (7/2))^2 = (1/4)
sqrt both sides
x + (7/2) = ±(1/2)
x = (-7/2) ± (1/2)
x = (-8/2) or (-6/2)
x = -4 or -3

ANS : -4 or -3