Answer:
(x-5)(x+4) = 0
Explanation:
Pre-Solving
Given
We are given the quadratic equation x²-x=20
And we want to factor it, meaning that we want to split it apart, usually to make it easier to solve.
Solving
First, let's subtract 20 from both sides, as when all 3 terms of a quadratic equation are on the same side, it makes it a lot easier to solve.
x² - x = 20
-20 -20
_______________
x² - x - 20 = 0
Now, we can get on to factoring.
In a quadratic equation, written as ax² + bx + c = 0 (like in here), b (the coefficient in front of just x, not x²) is equal to the sum of two numbers, while c is the product of the same two numbers.
The coefficient in front of x (b) is -1, and c is equal to -20.
Now think: which two numbers add up to -1, and multiply to equal -20?
Those numbers are -5 and 4.
Now, to factor a quadratic, we split it up into 2 binomials multiplied by each other, and each binomial is x + one of the numbers we found above. It looks like this: (x+1)(x+2). Remember that this only affects the left side; the right side stays the same.
In this case, we have -5 and 4, which will take the place of 1 and 2 in the example above.
Therefore, the factored form of x² - x - 20 = 0 is (x-5)(x+4) = 0.