(x%2B1)%3D(x-1)(x%2B3)-quadratic-equation.jpeg "(x-2)(x+1)=(x-1)(x+3) Quadratic Equation")
Solving the Quadratic Equation: (x-2)(x+1) = (x-1)(x+3)
This article will guide you through solving the quadratic equation (x-2)(x+1) = (x-1)(x+3). We'll break down the steps and explain the concepts involved.
1. Expanding the Equation
First, we need to expand both sides of the equation by applying the distributive property (FOIL method):
- Left side: (x-2)(x+1) = x² - x - 2
- Right side: (x-1)(x+3) = x² + 2x - 3
Now, our equation becomes: x² - x - 2 = x² + 2x - 3
2. Simplifying the Equation
Next, we can simplify the equation by moving all terms to one side:
- Subtract x² from both sides: -x - 2 = 2x - 3
- Subtract 2x from both sides: -3x - 2 = -3
- Add 2 to both sides: -3x = -1
3. Solving for x
Finally, we can solve for x by dividing both sides by -3:
- x = -1 / -3
- x = 1/3
Conclusion
Therefore, the solution to the quadratic equation (x-2)(x+1) = (x-1)(x+3) is x = 1/3.
This equation was relatively simple to solve because it simplified to a linear equation after expanding and simplifying. However, the same principles can be applied to more complex quadratic equations.