Question

SOLVE FOR X: (75 PTS)

x^2 - x - 20

Select the solutions to the problem. ONLY SELECT TWO ANSWERS. If you select more than two, your answer will be counted as wrong. *
0 points
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7

Answer 1

The value of x is -4 and 5.

Step by step explanation:

First, you have to let the expressions equals to 0 and elaborate the equation :

`{x}^(2) - x - 20 = 0`

`{x}^(2) + 4x - 5x - 20 = 0`

Next you have to factorize by taking out the like-terms :

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

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

Lastly, you can solve it :

`x - 5 = 0`

`x = 5`

`x + 4 = 0`

`x = - 4`

Answer 2

-4 and 5

Explanation:

When solving quadratic equations it's important to remember that they have 2 solution. We need to work out the factors, sum and the products to successfully factorise the quadratic and solve it. So,

x² - x - 20 = 0

Sum = -1

Product = -20

So we need two number that sum to -1 and multiply together to make -20

Factors = -5 and 4

x² - 5x + 4x - 20

Factor x² - 5x and 4x -20 separately

x² - 5x = x ( x - 5 )

4x - 20 = 4 ( x - 5 )

So

x ( x - 5 ) + 4 ( x - 5 )

We can see a common factor of ( x - 5 ) and the other bracket would be ( x + 4).

( x - 5 ) ( x + 4 )

But the question asks us for the solution so

x - 5 = 0

x = 5

x + 4 = 0

x = -4