-(2x-1)(x-3)%3D(x%2B5)(x-1).jpeg "(v) (2x-1)(x-3)=(x+5)(x-1)")
Solving the Equation: (2x-1)(x-3) = (x+5)(x-1)
In this article, we will solve the equation (2x-1)(x-3) = (x+5)(x-1). This equation involves multiplying binomials and simplifying the expressions. Let's break it down step by step.
Multiplying Binomials
The left side of the equation is (2x-1)(x-3). We can multiply the binomials using the distributive property:
2x(x-3) - 1(x-3)
2x^2 - 6x - x + 3
Combine like terms:
2x^2 - 7x + 3
Now, let's move on to the right side of the equation: (x+5)(x-1). Again, we apply the distributive property:
x(x-1) + 5(x-1)
x^2 - x + 5x - 5
Combine like terms:
x^2 + 4x - 5
Simplifying the Equation
Now, we can equate the two expressions:
2x^2 - 7x + 3 = x^2 + 4x - 5
Subtract x^2 from both sides to get:
x^2 - 7x + 3 = 4x - 5
Subtract 4x from both sides:
x^2 - 11x + 3 = -5
Add 5 to both sides:
x^2 - 11x + 8 = 0
This quadratic equation can be factored or solved using the quadratic formula.
Conclusion
In this article, we solved the equation (2x-1)(x-3) = (x+5)(x-1) by multiplying binomials and simplifying the expressions. The resulting quadratic equation x^2 - 11x + 8 = 0 can be solved further to find the roots of the equation.
