# 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.

1.  x = -2
2.  x = -3

## Step  1  :

#### Trying to factor by splitting the middle term

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 :

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 :

Solve  :    x+3 = 0

Subtract  3  from both sides of the equation :

x = -3

#### Solving a Single Variable Equation :

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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