(x-2)^2 = 5 solve for x??

(x - 2)^2 = 5
x - 2 = ±√5
x = ±√5 + 2

(x - 2) = ± √5
x = 2 ± √5

(x - 2)² = 5
x - 2 = 2.236068
x = 4.236068

Answer: x = 4.236068

Proof:
(4.236068 - 2)² = 5
2.236068² = 5
5 = 5

Since x is contained the the squared quantity and there's nothing else on that side of the equation, take the square root of both sides:

x - 2 = +/-(sqrt 5)

x = 2 +/- (sqrt 5) = answer

x=2±√5

Or even easier:
(x-2)^2=5
x-2=(+-)sqrt(5)
x = 2 (+-) sqrt(5)

i.e. the two solutions are 2-sqrt(5) and 2+sqrt(5)

(x-2)^2 = 5

(x-2) = +√5 or -√5

x = √5 + 2 = 4.24
or x = -√5 + 2 = -0.24

(x - 2)^2 = (x - 2) (x - 2)

x^2 - 4x + 4 = 5

x^2 - 4x - 1 = 0

Use quadratic formula to solve from here.....

The online version gives these results.....
x = -0.2360679774997898 or x = +4.23606797749979

http://www.math.com/students/calculators/source/quadratic.htm

Question Number 1 :
For this equation ( x - 2 ) * ( x - 2 ) = 5 , answer the following questions :
A. Calculate the Determinant ! Explain what it means !
B. Calculate the Roots ( x1 and x2 ) !

Answer Number 1 :
First, we must turn this equation ( x - 2 ) * ( x - 2 ) = 5 into a*x^2+b*x+c=0 form.
( x - 2 ) * ( x - 2 ) = 5 , expand the left hand side.
<=> x * ( x - 2 ) - 2 * ( x - 2 ) = 5
<=> x^2 - 4*x + 4 = 5 , move 5 from the right hand side to the left hand side.
<=> x^2 - 4*x + 4 - 5 = 0
<=> x^2 - 4*x - 1 = 0
The equation x^2 - 4*x - 1 = 0 is already in a*x^2+b*x+c=0 form.
So we can imply that the value of a = 1, b = -4, c = -1.

1A. Calculate the Determinant ! Explain what it means !
The formula Determinant = b^2-4*a*c is useful to solve this problem.
Since we know that a = 1, b = -4 and c = -1,
the value of a and b inside Determinant = b^2-4*a*c, can be subtituted using the values we know.
Which produce Determinant = (-4)^2 - 4 * (1)*(-1)
Which is the same with Determinant = 16+4
So we have the answer : Determinant = 20
Positive Determinant value, means that f(x) = x^2 - 4*x - 1 is going to intersect x axis in two points.

1B. Calculate the Roots ( x1 and x2 ) !
By using abc formula the value of x is both
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
We had know that a = 1, b = -4 and c = -1,
we need to subtitute a,b,c in the abc formula, with thos values.
So x1 = (-(-4) + sqrt( (-4)^2 - 4 * (1)*(-1)))/(2*1) and x2 = (-(-4) - sqrt( (-4)^2 - 4 * (1)*(-1)))/(2*1)
Which is the same with x1 = ( 4 + sqrt( 16+4))/(2) and x2 = ( 4 - sqrt( 16+4))/(2)
Which is can be turned into x1 = ( 4 + sqrt( 20))/(2) and x2 = ( 4 - sqrt( 20))/(2)
So we get x1 = ( 4 + 4.47213595499958 )/(2) and x2 = ( 4 - 4.47213595499958 )/(2)
So we got the answers as x1 = 4.23606797749979 and x2 = -0.23606797749979

Solution:


(x - 2)² = 5
x - 2 = ±√5

Adding 2 to both sides of the equation, it will give

x = 2 ±√5

hence, you will have two values of x

x = 2 + √5 --------------->> answer

and

x = 2 - √5 ----------------->> Answer