(x+2)(x+3)=x^2-10

Jasonbradley

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Jun 16, 2024

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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:

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

2. Subtract 6 from both sides: 5x = -16

3. 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.