Solve 2x^2-3x-5=0 Using Quadratic Formula

Quadratic equations are mathematical equations of the form ax^2 + bx + c = 0, where x is the variable, and a, b, and c are constants. One of the most useful tools in solving quadratic equations is the quadratic formula.

What Is The Quadratic Formula?

The quadratic formula is a formula that gives the solutions to any quadratic equation. In this article, we will discuss the quadratic formula and how to use it to solve quadratic equations.

The Quadratic Formula

The quadratic formula is given by:

x = (-b ± sqrt(b^2 – 4ac)) / 2a

This formula gives the solutions to any quadratic equation of the form ax^2 + bx + c = 0. The solutions to the quadratic equation are given by the values of x that satisfy the equation.

How to Use the Quadratic Formula

To use the quadratic formula, we need to follow a few steps:

• Step 1: Identify the values of a, b, and c in the quadratic equation.
• Step 2: Substitute the values of a, b, and c into the quadratic formula.
• Step 3: Simplify the expression inside the square root and evaluate it.
• Step 4: Solve for x by performing the operations indicated in the formula.

Let’s look at an example to see how the quadratic formula is used to solve quadratic equations.

Example: Solve the quadratic equation 2x^2 – 3x – 5 = 0 using the quadratic formula.

Step 1: Identify the values of a, b, and c in the quadratic equation.

In this case, a = 2, b = -3, and c = -5.

Step 2: Substitute the values of a, b, and c into the quadratic formula.

We get:

x = (-(-3) ± sqrt((-3)^2 – 4(2)(-5))) / 2(2)

Simplifying this expression gives us:

x = (3 ± sqrt(9 + 40)) / 4

x = (3 ± sqrt(49)) / 4

Step 3: Simplify the expression inside the square root and evaluate it.

The expression inside the square root simplifies to 49, so we have:

x = (3 ± 7) / 4

Step 4: Solve for x by performing the operations indicated in the formula.

We get two solutions:

x = (3 + 7) / 4 = 5/2

x = (3 – 7) / 4 = -1

Therefore, the solutions to the quadratic equation 2x^2 – 3x – 5 = 0 are x = 5/2 and x = -1.

Conclusion

In conclusion, the quadratic formula is a powerful tool for solving quadratic equations. It is important to follow the steps outlined above to use the formula correctly. By identifying the values of a, b, and c in the quadratic equation, substituting them into the quadratic formula, simplifying the expression inside the square root, and solving for x, we can find the solutions to any quadratic equation.