Quadratic Formula (x² = 2x + 4)?

Question

I worked on this for about an hour and can not figure out how to set this up, my book gives no real examples, can someone help?

x² = 2x + 4 (solve by using quadratic formula)

Answer 1

First rearrange
x²-2x-4=0
Use quadratic formula:
[ -b ± √(b² - 4ac) ] / (2a)
[-(-2) ± √( (-2)² - 4(1)(-4) ) ] / [ 2(1) ]
[2 ± √(4 + 16) ] /2
[2 ± √(20) ] /2
[2 ± 2√(5) ] /2
1 ± √(5)

1 + √(5) and
1 - √(5)

Answer 2

As an example, I'll solve x^2 - 5x = -4.

The quadratic formula is for equations of the form ax^2 + bx + c = 0, so we put it into this form by subtracting -2 from both sides, then factor the coefficients out of the terms for clarity:

x^2 - 5x = -4
x^2 - 5x + 4 = 0
1x^2 + -5x + 4 = 0

Here it's easy to see that a = 1, b = -5, and c = 4. We then plug these in:

(5 +- sqrt(25 - 4*1*4))/(2*1)
(5 +- sqrt(9))/2
(5 +- 3)/2
1 or 4

The solutions to my example, then, are 1 and 4. Your problem is solved in pretty much exactly the same way: make one side or the other 0, then plug the coefficients from the other side into the formula.

Also, remember that the "a" coefficient is always on the x^2 term, the "b" is always on the x term, and the "c" is always the constant term--don't be fooled by things such as 4 - 5x + x^2, which is the same thing as x^2 - 5x + 4.

Answer 3

x² - 2x - 4 = 0
x = [ 2 ± √(4 + 16) ] / 2
x = [ 2 ± √(20) ] / 2
x = [ 2 ± 2√5 ] / 2
x = 1 ± √5

Answer 4

x² - 2x - 4=0
--------------------------------
compare with ax^2 + bx + c=0
its roots are given by
x = {- b +- sqrt[b^2 - 4ac]} /2a
--------------------------
a=1, b= - 2, c= - 4
x = {2 +- sqrt[4 + 16]} /2
x = {2 +- sqrt[20]} /2
x = {2 +- 2 sqrt 5} /2
x = 1+- sqrt 5 >>> two values of x
x1 = 1+ sqrt 5
x2 = 1 - sqrt 5
equation is
[(x-1) - sqrt 5] [(x-1) + sqrt 5]
= [A - B] [A + B] = A^2 - B^2 = (x-1)^2 - 5 = x^2-2x+1-5
= given equation

Answer 5

the quadratic formula is -b+ or - the square root b squared-4ac over 2a

Answer 6

x^2 -2x-4=0 (se it equal to zero, then it's just the quadratic formula).

(x-2)(x+2)=0

X=2 or X=-2