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# How to solve an equation?Give a example and solve and please write the steps also.

5 months ago

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

-2*x^2-(-4)=0

## STEP1:Equation at the end of step 1

(0 - 2x2) - -4 = 0

## STEP3:Pulling out like terms

Pull out like factors :

4 - 2x2  =   -2 • (x2 - 2)

#### Trying to factor as a Difference of Squares:

Factoring:  x2 - 2

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 : 2 is not a square !!

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

#### Equation at the end of step3:

-2 • (x2 - 2) = 0

## STEP4:

#### Equations which are never true:

Solve :    -2   =  0

This equation has no solution.
A a non-zero constant never equals zero.

#### Solving a Single Variable Equation:

Solve  :    x2-2 = 0

Add  2  to both sides of the equation :

x2 = 2

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

x  =  ± √ 2

The equation has two real solutions

These solutions are  x = ± √= ± 1.4142

## Two solutions were found :

x = ± √= ± 1.4142