Answer:

x2-x-20=0

Two solutions were found :

x = 5

x = -4

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution :

Step 1 :

Trying to factor by splitting the middle term

1.1 FACTORING x2-x-20

The first term is, x2 its coefficient is 1 .

The middle term is, -x its coefficient is -1 .

The last term, "the constant", is -20

Step-1 : Multiply the coefficient of the first term by the constant 1 • -20 = -20

Step-2 : Find two factors of -20 whose sum EQUALS the coefficient of the middle term, which is -1 .

-20 + 1 = -19

-10 + 2 = -8

-5 + 4 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 4

x2 - 5x + 4x - 20

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

x • (x-5)

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

4 • (x-5)

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

(x+4) • (x-5)

Which is the desired factorization

Equation at the end of step 1 :

(x + 4) • (x - 5) = 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+4 = 0

Subtract 4 from both sides of the equation :

x = -4

Solving a Single Variable Equation :

2.3 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Supplement : Solving Quadratic Equation Directly

Solving x2-x-20 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula