Question

Solve each equation. 7x2 = 49

Answer 1

Answer:

Exact form : x = √7, -√7

Decimal form : x = 2.64575131... , -2.64575131...

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

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Answer 2

Answer:

 x = ± √7 = ± 2.6458

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 7x2 -  49  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  7x2 - 49  =   7 • (x2 - 7)  

Trying to factor as a Difference of Squares :

3.2      Factoring:  x2 - 7  

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 : 7 is not a square !!

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

Equation at the end of step  3  :

 7 • (x2 - 7)  = 0  

Step  4  :

Equations which are never true :

4.1      Solve :    7   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2      Solve  :    x2-7 = 0  

Add  7  to both sides of the equation :  

                     x2 = 7

 

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

                     x  =  ± √ 7  

The equation has two real solutions  

These solutions are  x = ± √7 = ± 2.6458