A Step-by-Step Guide to Solving Quadratic Equations using the Quadratic Formula

quadratic equations

Let’s start by understanding what quadratic equations are

Let’s start by understanding what quadratic equations are. A quadratic equation is a polynomial equation of degree 2, which means its highest power term is x^2. It has the standard form:

ax^2 + bx + c = 0

Here, “a”, “b”, and “c” are constants, and “x” is the variable in the equation. Our goal is to solve for “x” and find the values that make the equation true.

To solve a quadratic equation, there are several methods we can use: factoring, using the quadratic formula, completing the square, or graphing. I’ll explain the quadratic formula method, which is widely used.

The quadratic formula states that the solutions for “x” in a quadratic equation can be found using the following formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

Let’s go through an example to demonstrate how to use the quadratic formula:

Example:
Solve the quadratic equation 2x^2 – 5x + 2 = 0

In this equation, “a” is 2, “b” is -5, and “c” is 2. Plugging these values into the quadratic formula, we get:

x = (-(-5) ± √((-5)^2 – 4(2)(2))) / (2(2))
x = (5 ± √(25 – 16)) / 4
x = (5 ± √9) / 4

Now, let’s simplify further:

x = (5 ± 3) / 4

This gives us two possible solutions:

x1 = (5 + 3) / 4 = 8 / 4 = 2
x2 = (5 – 3) / 4 = 2 / 4 = 0.5

So, the solutions to the quadratic equation 2x^2 – 5x + 2 = 0 are x = 2 and x = 0.5.

Remember to always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

I hope this explanation helps! Let me know if you have any further questions.

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