(3x%2B5)-(x%2B3)%5E2%2B14%3D0.jpeg "(2x-1)(3x+5)-(x+3)^2+14=0")
Solving the Quadratic Equation: (2x-1)(3x+5)-(x+3)^2+14=0
In this article, we will solve the quadratic equation (2x-1)(3x+5)-(x+3)^2+14=0.
Expanding the Equation
First, let's expand the equation:
(2x-1)(3x+5) = 6x^2 + 7x - 5
-(x+3)^2 = -x^2 - 6x - 9
Now, let's add both expressions:
6x^2 + 7x - 5 - x^2 - 6x - 9 + 14 = 0
Simplifying the Equation
Combine like terms:
5x^2 + x - 0 = 0
Factoring the Equation
The equation can be factored as:
x(5x + 1) = 0
Solving for x
Now, let's solve for x:
x = 0 or 5x + 1 = 0
x = 0 or x = -1/5
Therefore, the solutions to the equation are x = 0 and x = -1/5.
Conclusion
In this article, we have successfully solved the quadratic equation (2x-1)(3x+5)-(x+3)^2+14=0. We expanded the equation, simplified it, factored it, and finally, solved for x. The solutions to the equation are x = 0 and x = -1/5.
