Solving the Equation: (x + 2)(x + 3) = x^2  10
This article will guide you through solving the equation (x + 2)(x + 3) = x^2  10.
Step 1: Expanding the Left Side
First, we need to expand the left side of the equation by multiplying the two binomials:
(x + 2)(x + 3) = x² + 3x + 2x + 6
Simplifying the expression:
x² + 3x + 2x + 6 = x² + 5x + 6
Step 2: Rewriting the Equation
Now we have:
x² + 5x + 6 = x²  10
Step 3: Solving for x
To solve for x, we need to isolate the variable:

Subtract x² from both sides: 5x + 6 = 10

Subtract 6 from both sides: 5x = 16

Divide both sides by 5: x = 16/5
Conclusion
Therefore, the solution to the equation (x + 2)(x + 3) = x²  10 is x = 16/5.