Solve x² - 8x - 20 = 0
x = 4, x = -5
x = -4, x = 5
x = 2, x = -10
x = -2, x = 10

Solution:

Let us factorize the quadratic equation to find the value of x by splitting the middle term.

Step 1: Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 1, b is the coefficient of x = - 8 and c is the constant term = - 20.

Step 2: Multiply a and c and find the factors that add up to b.

1 × (- 20) = - 20

⇒ - 10 and 2 are the factors that add up to b.

Step 3: Split bx into two terms.

x² - 10x + 2x - 20 = 0

Step 4: Take out the common factors by grouping.

x(x - 10) + 2 (x - 10) = 0

(x - 10) (x + 2) = 0

By putting the factors equal to zero we get two values of x

x - 10 = 0 and x + 2 = 0

x = 10 and x = - 2

Thus, the two values that satisfy the equation are 10 and - 2.

Solve x² - 8x - 20 = 0
x = 4, x = -5, x = - 4, x = 5, x = 2, x = -10, x = -2, x = 10

Summary:

The value of x for the equation x² - 8x - 20 = 0 is x = 10, - 2 which satisfies the equation.