Solve x2 - 3x - 4= 0 by completing the square.?

Question

please by de detailed

Answer 1

for reference you should write it as

x^2 - 3x - 4 = 0

Here's how to do it.

1. Preparing the equation

Move the 4 to the right hand side

x^2 - 3x = 4

2. Completing the square.

You simply take 1/2 of the coefficient in front of x (not x^2) and square it.

thus

(1/2) * 3 = 3/2
square it
(3/2)^2 = 9/4

We add this to both sides

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

x^2 - 3x +- 9/4 = 25/4

3. Solving through factoring.

Since we have completed the square, we know what the factor is gonna look like. The number term is simple the (1/2) coefficient of x we found earlier with a negative.

x^2 - 3x + 9/4 = (x - 3/2)^2 = 25/4

Square root both sides. When we do this, we realize that a plus or minus has to be in front of (x-3/2) since you do this when you are trying to solve a square.

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

Positive
x - 3/2 = s5/2
x = (3+5)/2
x = 4

Negative
-(x - 3/2) = sqrt(25/4)
x - 3/2 = - 5/2

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

Your two solutions are
x = 4, -1

Exactly the same as if you factored the original equation.

x^2 - 3x - 4 = 0 = (x - 4)(x+1)

Answer 2

completing the square:
(kay this will be my last detailed math lesson for you today :) )

x^2 - 3x -4 = 0
x^2- 3x + ___ = 4 (add the 4 to the other side)
x^2 - 3x - 2.25 = 4 + 2.25 (divide the middle number by two, then square it and then add it to the other side)
(x - 3/2)^2 = 6.25
Take the square root of both sides.
So it will be
x - 3/2 = 2.5 (2.5 is the square root of 6.25)
then add -3/2 to 2.5
The answer is 4.

THEN since you took the square root, you also have to do addition since it will be +/-
x + 3/2 = 2.5
Answer is 1.

Yay.
The end.
Please learn math, kay? :)

Answer 3

x^2 - 3x - 4 = 0

x^2 - 3x = 4 ------- Add 4 to both sides

x^2 - 3x + 2.25 = 4 + 2.25 ---- Add 2.25 to both sides to make a perfect square trinomial on the left. (2.25 = (3/2)^2)

(x - 1.5)^2 = 6.25 -------- Factor the right side.

x - 1.5 = +or- 2.5 ------- Take the square root of both sides (+or- means "plus or minus.")

x = 1.5 + 2.5 OR x = 1.5 - 2.5 ------ Add 1.5 to both sides.
x = 4 OR x = -1

Check:
x = 4
(4)^2 - 3(4) -4 = 16 - 12 - 4 = 4 - 4 = 0

x = -1
(-1)^2 - 3(-1) - 4 = 1 + 3 - 4 = 4 - 4 = 0

Answer 4

(x-4)(x+1)
x=4, -1

Answer 5

I hate math, but this is a good idea 2 get answers for your homework. Why do they make us learn this stuff. Unless you are becoming a math teacher or an engineer or something of that nature why would you need to know this? As long as you can count money your good. I can't help you.

Answer 6

x2 - 3x -4=0
(x+1)(x-4)=0
x= -1 or x=4

Does that help any?

Answer 7

so x2-3x-4=0. then u take half of 3 (1.5) and square that (2.25). so then it is x2-3x+2.25-2.25-4. then factor: (x-1.5)(x-1.5) -6.25. then it is (x-1.5)2 - 6.25. and then just solve for x. x = the square root of 6.25 and then plus 1.5.

Answer 8

Do your own damn homework.