How to solve quadratic equation by quadratic formula step by step?

The quadratic formula provides a direct method to solve quadratic equations of the form ax² + bx + c = 0. Here's a step-by-step guide:

Steps to Solve a Quadratic Equation Using the Quadratic Formula

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Step	Description
1. Identify a, b, and c	Rewrite the quadratic equation in the standard form: ax² + bx + c = 0. Identify the coefficients a, b, and c.
2. Substitute the values into the formula	Plug the values of a, b, and c into the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). According to the reference, this step involves direct substitution of the identified coefficients.
3. Simplify	Simplify the expression by performing the arithmetic operations, following the order of operations (PEMDAS/BODMAS). This includes simplifying the square root and the entire expression.

Let's solve the quadratic equation 2x² + 5x - 3 = 0 using the quadratic formula.

Identify a, b, and c:
- a = 2
- b = 5
- c = -3
Substitute into the quadratic formula:

x = (-5 ± √(5² - 4 2 -3)) / (2 * 2)
Simplify:

x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √49) / 4
x = (-5 ± 7) / 4

This gives us two possible solutions:
- x₁ = (-5 + 7) / 4 = 2 / 4 = 1/2
- x₂ = (-5 - 7) / 4 = -12 / 4 = -3

Therefore, the solutions to the quadratic equation 2x² + 5x - 3 = 0 are x = 1/2 and x = -3.