## The Quadratic Formula:

Now that we've established the foundation, let's unveil the quadratic formula:

**x = (-b ± √(b² - 4ac)) / (2a)**

### Step-by-step solution:

**Step 1: **Determine the Coefficients in

a: The coefficient of the quadratic term (ax^2).

b: The coefficient of the linear term (bx).

c: The constant term (c).

**Step 2: **Plug into the Formula

Now, substitute these coefficients into the quadratic formula

x = (-b ± √(b² - 4ac)) / (2a)

**Step 3:** Calculate the Discriminant

The term inside the square root, known as the discriminant (b² - 4ac), plays a crucial role in determining the nature of the solutions:

If the discriminant is positive, the equation has two distinct real roots.

If the discriminant is zero, the equation has one real root (a repeated root).

If the discriminant is negative, the equation has two complex roots.

**Step 4:** Compute the Roots

Use the formula to calculate the roots. Remember to consider both the positive and negative square root of the discriminant, as indicated by the ± symbol:

x1 = (-b + √(b² - 4ac)) / (2a)

x2 = (-b - √(b² - 4ac)) / (2a)

**Related:** Quadratic Formula: A Step-by-Step Guide to Solving Quadratic Equations:

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