(x-5)-2x%5E2%2B10x-25%3D0.jpeg "(2x-1)(x-5)-2x^2+10x-25=0")
Solving the Equation: (2x-1)(x-5)-2x^2+10x-25=0
This article will guide you through solving the equation (2x-1)(x-5)-2x^2+10x-25=0. We'll break down the steps and provide explanations to make the process clear.
Step 1: Expanding the Equation
First, we need to expand the equation by multiplying the terms within the parentheses:
(2x-1)(x-5) = 2x^2 - 10x - x + 5 = 2x^2 - 11x + 5
Now, the equation becomes:
2x^2 - 11x + 5 - 2x^2 + 10x - 25 = 0
Step 2: Simplifying the Equation
Next, we can combine like terms to simplify the equation:
-x - 20 = 0
Step 3: Isolating the Variable
To isolate the variable 'x', we need to move the constant term to the other side of the equation. We can do this by adding 20 to both sides:
-x = 20
Step 4: Solving for 'x'
Finally, to find the value of 'x', we need to multiply both sides of the equation by -1:
x = -20
Conclusion
Therefore, the solution to the equation (2x-1)(x-5)-2x^2+10x-25=0 is x = -20.