Solving the Equation (x+10)(x10) = 300
This equation presents a quadratic equation in disguise, and we can solve it by following these steps:
1. Expanding the Equation
First, we need to expand the left side of the equation using the difference of squares pattern: (x + 10)(x  10) = x²  10² = x²  100
This gives us the simplified equation: x²  100 = 300
2. Rearranging the Equation
Now, we move the constant term to the right side of the equation: x² = 300 + 100
This simplifies to: x² = 400
3. Solving for x
To isolate x, we take the square root of both sides: √x² = ±√400
This gives us two possible solutions: x = ±20
Therefore, the solutions to the equation (x+10)(x10) = 300 are x = 20 and x = 20.
Verification
We can verify our solutions by plugging them back into the original equation:

For x = 20: (20 + 10)(20  10) = 30 * 10 = 300

For x = 20: (20 + 10)(20  10) = (10) * (30) = 300
Both solutions satisfy the original equation, confirming our results.