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 :

- x = -2
- x = -3

## Step by step solution :

## Step 1 :

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

1.1 Factoring x

The first term is, x

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 .

^{2}+5x+6The first term is, x

^{2}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

x

^{2}+ 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.

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 :

#### Solving a Single Variable Equation :

### Supplement : Solving Quadratic Equation Directly

`Solving x`^{2}+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

Visit TIGER ALGEBRA.

Visit TIGER ALGEBRA.

Here's a site for solving equations:

## 0 komentar

## Post a Comment