Solving the Equation: 5(1-x)^2-6(x^2-3x-7)=x(x-3)-2x(x+5)-2
In this article, we will solve the equation 5(1-x)^2-6(x^2-3x-7)=x(x-3)-2x(x+5)-2.
Step 1: Expand the Equation
Let's start by expanding the equation:
5(1-x)^2 - 6(x^2 - 3x - 7) = x(x-3) - 2x(x+5) - 2
Expanding the left side of the equation, we get:
5 - 10x + 5x^2 - 6x^2 + 18x + 42 = x(x-3) - 2x(x+5) - 2
Step 2: Simplify the Equation
Simplifying the left side of the equation, we get:
-x^2 + 8x + 47 = x(x-3) - 2x(x+5) - 2
Step 3: Expand the Right Side of the Equation
Expanding the right side of the equation, we get:
-x^2 + 3x - 2x^2 - 10x - 2 = 0
Step 4: Combine Like Terms
Combine like terms on the right side of the equation:
-3x^2 - 7x - 2 = 0
Step 5: Factor the Equation (Optional)
If we want to factor the equation, we can do so:
-(3x+1)(x+2) = 0
This gives us two possible solutions:
x = -1/3 and x = -2
However, we can also leave the equation in its quadratic form:
-3x^2 - 7x - 2 = 0
Conclusion
In this article, we have successfully solved the equation 5(1-x)^2-6(x^2-3x-7)=x(x-3)-2x(x+5)-2. We expanded the equation, simplified it, and combined like terms to get a quadratic equation. We also had the option to factor the equation, which gave us two possible solutions.
