Find the solutions(s) to 9x^2-54x=0

Two solutions were found :

x = 6

x = 0

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 32x2 -  54x  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  9x2 - 54x  =   9x • (x - 6)  

Equation at the end of step  3  :

 9x • (x - 6)  = 0  

Step  4  :

Theory - Roots of a product :

4.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.2      Solve  :    9x = 0  

Divide both sides of the equation by 9:

                    x = 0  

Solving a Single Variable Equation :

4.3      Solve  :    x-6 = 0  

Add  6  to both sides of the equation :  

                     x = 6

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

b.

step-by-step explanation: