Jasonbradley
Home

(x+3)(x+4)=(x+1)(x+2)

2 min read Jun 16, 2024
(x+3)(x+4)=(x+1)(x+2)

Solving the Equation: (x+3)(x+4) = (x+1)(x+2)

This equation presents a simple quadratic equation that can be solved using a few algebraic steps. Let's break down the process:

Expanding the Equation

First, we need to expand both sides of the equation using the FOIL (First, Outer, Inner, Last) method:

  • Left Side: (x+3)(x+4) = x² + 4x + 3x + 12 = x² + 7x + 12
  • Right Side: (x+1)(x+2) = x² + 2x + x + 2 = x² + 3x + 2

Now our equation looks like this: x² + 7x + 12 = x² + 3x + 2

Simplifying the Equation

Next, we need to simplify the equation by combining like terms and bringing all terms to one side:

  • Subtract x² from both sides: 7x + 12 = 3x + 2
  • Subtract 3x from both sides: 4x + 12 = 2
  • Subtract 12 from both sides: 4x = -10

Solving for x

Finally, we can solve for x by dividing both sides by 4:

  • x = -10/4 = -5/2

Conclusion

Therefore, the solution to the equation (x+3)(x+4) = (x+1)(x+2) is x = -5/2.

Related Post

Featured Posts