Solving the Equation: 2x^2 - 17x - 30
In this article, we will explore the solution to the quadratic equation 2x^2 - 17x - 30. This equation is a type of polynomial equation where the highest power of the variable (x) is 2.
Understanding the Equation
The equation 2x^2 - 17x - 30 can be broken down into three parts:
- 2x^2: This is the quadratic term, where x is squared and multiplied by 2.
- -17x: This is the linear term, where x is multiplied by -17.
- -30: This is the constant term, which is -30.
Factoring the Equation
To solve the equation, we can try to factor it into the product of two binomials. Factoring is a process of finding two expressions that multiply to give the original equation.
After examining the equation, we can find that it can be factored as:
2x^2 - 17x - 30 = (2x + 5)(x - 6) = 0
Solving for x
Now that we have factored the equation, we can equate each factor to zero and solve for x.
(2x + 5) = 0
Subtracting 5 from both sides gives:
2x = -5
Dividing both sides by 2 gives:
x = -5/2
(x - 6) = 0
Adding 6 to both sides gives:
x = 6
Therefore, the solutions to the equation 2x^2 - 17x - 30 are x = -5/2 and x = 6.
Conclusion
In this article, we have seen how to solve the quadratic equation 2x^2 - 17x - 30 by factoring it into the product of two binomials. We have found that the solutions to the equation are x = -5/2 and x = 6.
