Friday, July 20, 2018

Equation Calculator Site


The equations in mathematics are open sentences that have truth, right or wrong values. For example linear equations one variable: $2x-1=3$, linear equations two variables: $x+2y=4$, quadratic equations: $x^2+5x+6=0$, and others. 

When discussing an equation in mathematics, it also discusses how to solve the equation. For example, the equation $ x ^ 2 + 5x + 6 = 0 $ has a solution $ x_1 = -2 $ or $ x_2 = -3 $. How to solve it? One of the sites discussing the settlement and how to solve equations is tiger algebra.


Two solutions were found :

  1.  x = -2
  2.  x = -3

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x2+5x+6

The first term is,  x2  its coefficient is  1 .
The middle term is,  +5x  its coefficient is  5 .
The last term, "the constant", is  +6 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 6 = 6

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   5 .
     -6   +   -1   =   -7
     -3   +   -2   =   -5
     -2   +   -3   =   -5
     -1   +   -6   =   -7
     1   +   6   =   7
     2   +   3   =   5   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  3 
                     x2 + 2x + 3x + 6

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x+2)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x+2)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (x+2)
             Which is the desired factorization

Equation at the end of step  1  :

  (x + 3) • (x + 2)  = 0 

Step  2  :

Theory - Roots of a product :

 2.1    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 :

 2.2      Solve  :    x+3 = 0

 
Subtract  3  from both sides of the equation :
 
                     x = -3 

Solving a Single Variable Equation :

 2.3      Solve  :    x+2 = 0

 
Subtract  2  from both sides of the equation :
 
                     x = -2 

Supplement : Solving Quadratic Equation Directly

Solving    x2+5x+6  = 0   directly 

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

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