completing the square? x^2 - 2x -3 = 0?

Question

I can use some help in understanding the steps than just finding the answer, thanks.

The answer reads x = 3, x = -1

just trying to underdtand how we get them.

Answer 1

First: move the last term to the right side - add 3 to both sides (when you move a term to the opposite side, always use the opposite sign).

x^2 - 2x -3 +3 = 0+3
x^2 - 2x __ = 3

Sec: take the 2nd term & divide it by 2; then square the result.

-2/2 = -1
(-1)^2 = 1*1 = 1

*Now, add 1 to both sides of the equation.

x^2 - 2x + 1 = 3 + 1
x^2 - 2x + 1 = 4

Third: factor the expression on the left & you should get...

(x-1)(x-1) = 4
(x-1)^2 = 4

If your solving for "x" - find the square root of both sides.

V`(x-1)^2 = +/- V`(4)
x - 1 = +/- 2
Add 1 to both sides.

x - 1 + 1 = +/- 2 + 1
x = +/- 2+1
x = -2+1 = -1
x = -2-1 = -3

Solutions: -1, -3

Answer 2

x^2 - 2x - 3 = 0
now since coeff of x is 2 we know that the final sq shud have (x-1)^2 since its equal to x^2 - 2x - 1.

therefore x^2 - 2x - 3 = 0
becomes
(x^2 - 2x + 1) -4 = 0
(x - 1)^2 - 4 = 0
x - 1 = (+or- )sqrt(4)
x = 1 (+or-) 2
x = 3 or -1

Answer 3

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

Answer 4

find two numbers a and b with the property that
a*b = -3
and a + b = -2
a = 1, b = -3

have this property
next write down :
x^2 - 2x -3 = (x-1)(x+3) = 0
thus x =1 or x =2 -3 are the solutions of your
equation

so what was the question ?
..

Answer 5

(x² - 2x + 1) - 1 - 3 = 0
(x - 1)² = 4
x - 1 = ± 2
x = 3 , x = - 1