Question

How to find the square root of 5x-25=0

Answer 1

Answer:

   x = ± √5 = ± 2.2361

Step-by-step explanation:

Two solutions were found :

                  x = ± √5 = ± 2.2361

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 5x2 -  25  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  5x2 - 25  =   5 • (x2 - 5)  

Trying to factor as a Difference of Squares :

3.2      Factoring:  x2 - 5  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.  

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!  

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  3  :

 5 • (x2 - 5)  = 0  

Step  4  :

Equations which are never true :

4.1      Solve :    5   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2      Solve  :    x2-5 = 0  

Add  5  to both sides of the equation :  

                     x2 = 5  

 

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 5  

              x = ± √5 = ± 2.2361