2-5(x-2)-(2x%2B3)2-(5x%2B2)(x-1)%3D0.jpeg "(3x-1)2-5(x-2)-(2x+3)2-(5x+2)(x-1)=0")
Solving the Quadratic Equation: (3x-1)2-5(x-2)-(2x+3)2-(5x+2)(x-1)=0
In this article, we will solve the quadratic equation (3x-1)2-5(x-2)-(2x+3)2-(5x+2)(x-1)=0. To solve this equation, we will use algebraic manipulation and factoring techniques.
Step 1: Expand the Equation
Let's start by expanding the equation:
(3x-1)2 = 9x2 - 6x + 1 -5(x-2) = -5x + 10 -(2x+3)2 = -4x2 - 12x - 9 -(5x+2)(x-1) = -5x2 - x + 2
Now, let's combine like terms:
9x2 - 6x + 1 - 5x + 10 - 4x2 - 12x - 9 - 5x2 - x + 2 = 0
Combine like terms:
-10x2 + 17x - 6 = 0
Step 2: Factor the Equation
Now, let's try to factor the quadratic equation:
-10x2 + 17x - 6 = -(10x2 - 17x + 6) = -(5x - 3)(2x - 2) = 0
Step 3: Solve for x
Now that we have factored the equation, we can solve for x:
(5x - 3)(2x - 2) = 0
This gives us two possible solutions for x:
Solution 1:
5x - 3 = 0 --> 5x = 3 --> x = 3/5
Solution 2:
2x - 2 = 0 --> 2x = 2 --> x = 1
Therefore, the solutions to the equation (3x-1)2-5(x-2)-(2x+3)2-(5x+2)(x-1)=0 are x = 3/5 and x = 1.
