(x%2B4)%3Dx%5E2%2B4.jpeg "(x-3)(x+4)=x^2+4")
Solving the Equation (x-3)(x+4) = x^2 + 4
This equation involves expanding and simplifying expressions, and ultimately, solving for the value of x. Let's break down the steps:
1. Expanding the Left Side
We begin by expanding the left side of the equation using the FOIL method:
- First: x * x = x²
- Outer: x * 4 = 4x
- Inner: -3 * x = -3x
- Last: -3 * 4 = -12
Putting it all together: (x - 3)(x + 4) = x² + 4x - 3x - 12
2. Simplifying the Equation
Now we can simplify the equation by combining like terms:
x² + 4x - 3x - 12 = x² + 4
This simplifies to: x² + x - 12 = x² + 4
3. Isolating the Variable
Next, we aim to isolate the x term. Subtracting x² from both sides, we get:
x - 12 = 4
4. Solving for x
Finally, we solve for x by adding 12 to both sides:
x = 16
Conclusion
Therefore, the solution to the equation (x - 3)(x + 4) = x² + 4 is x = 16.