Solve X squared-x-20 equals 0

Answer 1

It is a quadratic equation and there are few ways to solve em

(Before we start note that the values of x in a quadratic equations are called roots or zeroes or solution)

1. Mid term split method
2. Quadratic formula

Lets try both:

• x^2 -x -20 = 0 can be split as x^2 -5x + 4x - 20 = 0

Taking terms common,

x(x-5) + 4(x-5) =0

(x-5)(x+4)=0

For this expression to be 0, either of the two numbers must be 0 since anything multiplied with 0 is 0.

So it can either be

(0)(x+4) = 0 Which is true or (x-5)(0) = 0 which is true too

When (x-5) = 0, x=5 and when (x+4) = 0 , x= -4

So we have two solutions 5,-4

• For the quadratic formula there's a long formula for roots which is

{-b ± √(b² - 4ac)}/2a

Where the quadratic equation is ax² + bx +c =0,

Here a= 1, b = -1 and c = -20,

Substituting the values in the formula :

[-(-1) ± √{(-1)² - 4(1)(-20)}]/2(1)

={1 ± √(1 +80)}/2

=(1 ± √81)/2

=(1 ± 9)/2

2 answers are possible from here on,

(1 + 9)/2 and (1 - 9)/2

which are 10/2 = 5 and -8/2=-4

Look we same answer from both methods.