Solving Quadratic Equations: Understanding the Quadratic Formula and How to Find Solutions

Quadratic Formula

The quadratic formula is a mathematical equation used to find the solutions, or roots, of a quadratic equation

The quadratic formula is a mathematical equation used to find the solutions, or roots, of a quadratic equation. It is given by:

x = (-b ± √(b^2 – 4ac)) / (2a)

In this formula, “x” represents the variable we are trying to solve for, while “a”, “b”, and “c” are coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

To use the quadratic formula, follow these steps:

Step 1: Identify the coefficients a, b, and c from the quadratic equation.

Step 2: Substitute these values into the quadratic formula.

Step 3: Simplify the expression inside the square root, which is called the discriminant (b^2 – 4ac).

Step 4: Calculate the square root of the discriminant.

Step 5: Use the “±” symbol to denote two possible solutions, one with a positive square root result and the other with a negative square root result.

Step 6: Divide the expression outside the square root by 2a.

Step 7: Simplify and calculate both solutions, taking into account the positive or negative square root result.

For example, let’s say we have the quadratic equation 2x^2 + 5x – 3 = 0. Applying the quadratic formula:

a = 2, b = 5, c = -3

Plugging these values into the formula:

x = (-5 ± √(5^2 – 4(2)(-3))) / (2(2))

Simplifying:

x = (-5 ± √(25 + 24)) / 4

x = (-5 ± √49) / 4

Since √49 = 7:

x = (-5 ± 7) / 4

This gives us two possible solutions:

x = (-5 + 7) / 4 = 2/4 = 1/2

x = (-5 – 7) / 4 = -12/4 = -3

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

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