how do i solve by completing the square?

Question

x^2 + 3x = 4

Answer 1

take the coefficient of x and half it, then square it

so that is 3/2, squaring it we have 9/4

now add that to both sides

x^2 + 3x + 9/4 = 4 + 9/4

now the left hand side is a perfect square

(x+ 3/2)^2 = 25 / 4

taking the square root of both sides we have

x + 3/2= +- 5/2

so x = (-3+-5)/2

x=-4 or x = 1

Answer 2

You must add a constant c that will make x²+3x+c factorable into the square of a binomial. To find this constant, consider the formula for square of a sum:

(a+b)²=a²+2ab+b²

Now x=a, and you must figure out b:

2ab=3x
2b=3
b=3/2

Therefore, you must add (3/2)²=9/4 to both sides of your equation. This will turn the left side into the square of a binomial:

x²+3x+9/4=4+9/4
(x+3/2)²=25/4

Now take the square root of both sides:

x+3/2=±5/2
x=-3/2±5/2
x=1 or x=-4

Check:

1²+3(1)=4
1+3=4

(-4)²+3(-4)=4
16-12=4

Answer 3

It's hard to explain here, but I'll try.

(If there was a leading coefficient, you would divide it out before this stage.)

Put in a blank.

(x^2 + 3x + ___ ) = 4

In the blank: (b/2)^2 [FYI: b is the coefficient of the second term in the trinomial]
Whatever you put in the blank, you have to add to the other side to keep it balanced. (If there were a leading coefficient that you had divided out, you would multiply, then add that number to other side.)

(x^2 + 3x + (9/4)) = 4 + 9/4

(x + __ )^2 = 16/4 + 9/4

The sign that goes in the binomial is the same as the sign on b.
In this blank: b/2 from your first trinomial

(x + (3/2))^2 = 25/4

Solve for x. Remember, since it's a square root, you have to do plus or minus.

x + 3/2 = (+/-)5/2

x = 5/2 - 3/2 = 2/2 = 1

x = -5/2 - 3/2 = -8/2 = -4

x = 1 or -4

Answer 4

To find the constant value to add to both sides, divide the linear term by 2 and square it.

(3/2)^2 = 9/4.

Add 9/4 to both sides:

x^2 + 3x + 9/4 = 4+9/4

Factor the quadratic as a perfect square binomial:

(x+3/2)^2 = 25/4

Take the square root of both sides

x+3/2 = +/-sqrt(25/4)

x + 3/2 = +/- 5/2

Solve for x:

x = 1 or -4.

Answer 5

x² + 3x + 9/4 = 4 + 9/4
(x + 3/2)² = 25/4
x + 3/2 = ± 5/2
x = - 3/2 ± 5/2
x = 1 , x = - 4

Answer 6

Take half of 3x and square it (3/2)^2
x^2+3x+9/4=4+9/4

(x+3/2)^2=25/4
sq.rt (x+3/2)^2=sq.rt25/4
x+3/2=+(-)5/2
x=-3/2+5/2 or -3/2-5/2
x=1 or x=-4