(4x-29)%3D(2x-5)(2x-17)%2B1.jpeg "(x-7)(4x-29)=(2x-5)(2x-17)+1")
Solving the Equation: (x-7)(4x-29)=(2x-5)(2x-17)+1
This article will guide you through the process of solving the given equation: (x-7)(4x-29) = (2x-5)(2x-17) + 1. We will break down the steps involved and arrive at the final solution.
Expanding the Equation
The first step is to expand both sides of the equation by multiplying out the brackets:
- Left side: (x-7)(4x-29) = 4x² - 29x - 28x + 203 = 4x² - 57x + 203
- Right side: (2x-5)(2x-17) + 1 = 4x² - 34x - 10x + 85 + 1 = 4x² - 44x + 86
Now the equation becomes: 4x² - 57x + 203 = 4x² - 44x + 86
Simplifying the Equation
Since both sides of the equation have a term of 4x², we can subtract this term from both sides, leaving us with:
-57x + 203 = -44x + 86
Now, we need to isolate the x terms on one side of the equation. Adding 44x to both sides, we get:
-13x + 203 = 86
Subtracting 203 from both sides gives us:
-13x = -117
Solving for x
Finally, we can solve for x by dividing both sides by -13:
x = 9
Therefore, the solution to the equation (x-7)(4x-29) = (2x-5)(2x-17) + 1 is x = 9.