(x%2B4)-(x-3)(x-5)%3D2.jpeg "(x+3)(x+4)-(x-3)(x-5)=2")
Solving the Equation (x+3)(x+4)-(x-3)(x-5)=2
This article will guide you through the steps to solve the equation (x+3)(x+4)-(x-3)(x-5)=2.
Expanding the Equation
First, we need to expand the equation by multiplying out the brackets:
- (x+3)(x+4) = x² + 7x + 12
- (x-3)(x-5) = x² - 8x + 15
Now, the equation becomes: x² + 7x + 12 - (x² - 8x + 15) = 2
Simplifying the Equation
Next, we can simplify the equation by removing the brackets and combining like terms:
x² + 7x + 12 - x² + 8x - 15 = 2 15x - 3 = 2
Isolating the Variable
To isolate the variable x, we need to move the constant term to the right side of the equation:
15x = 2 + 3 15x = 5
Solving for x
Finally, we can solve for x by dividing both sides of the equation by 15:
x = 5 / 15 x = 1/3
Solution
Therefore, the solution to the equation (x+3)(x+4)-(x-3)(x-5)=2 is x = 1/3.