Use matrix operations and substitution to determine which of the following numerical values for z can be substituted into the second equation to solve for y?

x2-5x=14

Two solutions were found :

x = 7

x = -2

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".

Rearrange:

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

                    x^2-5*x-(14)=0

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-5x-14

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -14

Step-1 : Multiply the coefficient of the first term by the constant   1 • -14 = -14

Step-2 : Find two factors of  -14  whose sum equals the coefficient of the middle term, which is   -5 .

     -14    +    1    =    -13

     -7    +    2    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  2

                    x2 - 7x + 2x - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-7)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-7)

Step-5 : Add up the four terms of step 4 :

                   (x+2)  •  (x-7)

            Which is the desired factorization

Equation at the end of step  1  :

 (x + 2) • (x - 7)  = 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.

Solving a Single Variable Equation :

2.2      Solve  :    x+2 = 0

Subtract  2  from both sides of the equation :

                     x = -2

Solving a Single Variable Equation :

2.3      Solve  :    x-7 = 0

Add  7  to both sides of the equation :

                     x = 7

Step-by-step explanation:

But the answer is x =7