Question

X(x-1)-(x-21) (x-2)=1-21

Answer 1

x²-x-(x-2x-21x+42)=-20

x²-x-(x²-23x+42)=-20

x²-x-x²+23x-42=-20

22x-42=-20

22x=-20+42

22x=22

x=1

Answer 2

To solve the given equation $X(x-1) - (x-21)(x-2) = 1 - 21$, we can follow these steps:

1. Distribute the terms on both sides of the equation: $X(x) - X(1) - (x^2 - 2x - 21x + 42) = -20$

2. Simplify each term: $X(x) - X - x^2 + 23x - 42 = -20$

3. Combine like terms: $X(x) - x^2 + 23x - X - 42 = -20$

4. Combine the terms involving $X$: $X(x) - X = X(x - 1)$

5. Combine the terms involving $x$: $- x^2 + 23x$

6. Rearrange the equation: $X(x - 1) - x^2 + 23x - 42 = -20$

7. Combine the terms on the left side: $X(x - 1) - x^2 + 23x - 42 + 20 = 0$

8. Simplify further: $X(x - 1) - x^2 + 23x - 22 = 0$

At this point, we have a quadratic equation in terms of $x$. The equation is non-linear and cannot be simplified any further algebraically. To solve for $x$, we can either use numerical methods or a calculator. The exact solution for $x$ will likely involve decimal values.

If you provide a specific value for $X$, I can help you solve for $x$ numerically using methods like factoring, completing the square, or using the quadratic formula.