SOLUTION: can i please have help to solve this? (x-1)^2=5

Question 81000: can i please have help to solve this?
(x-1)^2=5
Found 2 solutions by praseenakos@yahoo.com, bucky:
Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
QUESTION:

(x-1)^2=5

SOLUTION:

At first expand the expression using the identity (a-b)^2 = a^2 - 2ab + b^2 as follows............

(X-1)^2 = 5

==> x^2 - 2x + 1 = 5

subtract 5 from both sides

==> x^2 - 2x + 1 - 5 = 5 - 5

==> x^2 - 2x - 5 = 0

This is a quadratic equation so we can solve it using quadratic formula.

comparing with the standard equation, ax^2 + bx + c = 0, we have,

a = 1 b = -2 and c = -5

So solution is given by,

==> x = (2 + 4.9)/2 or x = (2-4.9)/2

==> x = 6.9/2 or x = -2.9/2

==> x = 3.45 or x = -1.45

To check your solution, substitute any of these values for x in the given equation, you will get tha answer 5, which is in the right hand side.

Hope you found this explanation useful.

Regards.

Praseena.

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
Square the left side and the equation becomes:
.

.
Then get this equation into standard quadratic form by eliminating the 5 on the right side
so that the right side becomes 0. Do this by subtracting 5 from both sides. When you do
that subtraction the equation becomes:
.

.
The left side of this equation does not factor nicely. So use the quadratic formula. This
formula says that for a quadratic equation of the standard form:
.

.
The values of x that satisfy this equation are given by the equation:
.

.
By comparing our equation with the standard form you can see that a = 1, b = -2, and c = -4.
.
By substituting these values into the equation that defines the values of x you get:
.

.
This simplifies to:
.

.
Note that
.
Substituting for reduces the equation for x to:
.

.
So this problem has two solutions for x ... and
.
Hope this helps you to understand the problem a little better.
.
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