(x+1)(x+2)=(x-2)(x+2)

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (x+1)(x+2) = (x-2)(x+2)

This equation presents a simple quadratic equation with a unique solution. Here's how to solve it:

Expanding the Equation

First, we need to expand both sides of the equation using the distributive property (also known as FOIL):

• Left Side: (x+1)(x+2) = x² + 2x + x + 2 = x² + 3x + 2
• Right Side: (x-2)(x+2) = x² + 2x - 2x - 4 = x² - 4

Now our equation looks like this: x² + 3x + 2 = x² - 4

Simplifying and Solving

We can simplify this further by subtracting x² from both sides:

3x + 2 = -4

Next, subtract 2 from both sides:

3x = -6

Finally, divide both sides by 3:

x = -2

Solution

Therefore, the solution to the equation (x+1)(x+2) = (x-2)(x+2) is x = -2.

Checking the Solution

We can check our answer by plugging x = -2 back into the original equation:

• Left Side: (-2 + 1)(-2 + 2) = (-1)(0) = 0
• Right Side: (-2 - 2)(-2 + 2) = (-4)(0) = 0

Since both sides equal 0, our solution is correct.