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

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

Grade:7

1 Answers

Priyanshu Singh
37 Points
5 months ago

Solve--2x^2=-4

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 

Step by step solution :

STEP1:Equation at the end of step 1

(0 - 2x2) - -4 = 0

STEP2:

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   4 - 2x2  =   -2 • (x2 - 2) 

 

Trying to factor as a Difference of Squares:

 3.2      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:

 4.1      Solve :    -2   =  0

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

 

Solving a Single Variable Equation:

 4.2      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

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