Question

¿Cual es la solución (Puntos de intersección en el eje x) de la siguiente ecuación cuadrática 2x^2-8=0?

Answer 1

Respuesta:

2x2-8=0  

Two solutions were found :

x = 2

x = -2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 2x2 -  8  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  2x2 - 8  =   2 • (x2 - 4)  

Trying to factor as a Difference of Squares :

3.2      Factoring:  x2 - 4  

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 : 4 is the square of 2

Check :  x2  is the square of  x1  

Factorization is :       (x + 2)  •  (x - 2)  

Equation at the end of step  3  :

 2 • (x + 2) • (x - 2)  = 0  

Step  4  :

Theory - Roots of a product :

4.1    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.

Equations which are never true :

4.2      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.3      Solve  :    x+2 = 0  

Subtract  2  from both sides of the equation :  

                     x = -2

Solving a Single Variable Equation :

4.4      Solve  :    x-2 = 0  

Add  2  to both sides of the equation :  

                     x = 2

Two solutions were found :

x = 2

x = -2

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