# Quadratic Formula Calculator

TLDRThis video demonstrates how to use a quadratic formula calculator to solve equations like x^2 + 4x + 3 = 0. The solution is calculated as x = -1 or x = -3. The video walks through the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. It explains how to identify the values of a, b, and c from the equation and shows step-by-step how to substitute these values into the formula. By breaking down the process, it simplifies solving quadratic equations by hand and using a calculator.

### Takeaways

- 📐 The video is about using a quadratic formula calculator.
- 🧮 The example given is solving the equation x^2 + 4x + 3 = 0.
- 💻 The speaker inputs the equation into the calculator, and the solution provided is x = -1 or x = -3.
- 🔢 The quadratic formula is explained as x = (-b ± √(b² - 4ac)) / 2a.
- 🅰️ The coefficients in the equation are identified as a = 1, b = 4, and c = 3.
- 📊 These values are plugged into the quadratic formula for solving.
- 🧠 The discriminant (b² - 4ac) is calculated: 16 - 12 = 4.
- ✔️ The square root of 4 is 2, leading to two possible solutions.
- ➕ The first solution is x = (-4 + 2) / 2, which simplifies to x = -1.
- ➖ The second solution is x = (-4 - 2) / 2, which simplifies to x = -3.

### Q & A

### What equation is solved in the video?

-The equation solved is x^2 + 4x + 3 = 0.

### How does the quadratic formula solve for x?

-The quadratic formula is x = (-B ± √(B^2 - 4AC)) / 2A.

### What are the values of A, B, and C for the equation x^2 + 4x + 3 = 0?

-A = 1, B = 4, and C = 3.

### What is B^2 - 4AC in this case?

-B^2 - 4AC = 16 - 12 = 4.

### What is the square root of B^2 - 4AC?

-The square root of 4 is 2.

### How is the first solution for x calculated?

-The first solution is x = (-4 + 2) / 2, which simplifies to x = -1.

### How is the second solution for x calculated?

-The second solution is x = (-4 - 2) / 2, which simplifies to x = -3.

### What does the calculator provide as the solutions?

-The calculator provides x = -1 or x = -3.

### Why are there two possible solutions for x?

-There are two solutions because of the ± in the quadratic formula, leading to a positive and a negative result.

### What is the purpose of the video?

-The purpose of the video is to explain how to use a quadratic formula calculator and walk through solving a quadratic equation by hand.

### Outlines

### 📐 Introduction to Using the Quadratic Formula Calculator

This paragraph introduces the video tutorial on using a quadratic formula calculator. It starts with the problem x² + 4x + 3 = 0, showing how to input the equation into the calculator to obtain the result. The calculator determines that the solution is x = -1 or x = -3. The presenter then hints at explaining the manual steps for solving the equation using the quadratic formula.

### ✏️ Understanding the Quadratic Formula and Variable Identification

This paragraph explains the quadratic formula and how it applies to equations of the form ax² + bx + c = 0. The formula is given as x = [-b ± √(b² - 4ac)] / 2a. The presenter identifies the values of a, b, and c from the equation x² + 4x + 3 = 0. Specifically, a is the coefficient of x² (which is 1), b is the coefficient of x (4), and c is the constant (3).

### 🔍 Applying the Quadratic Formula with a = 1, b = 4, and c = 3

Here, the presenter plugs the values of a, b, and c into the quadratic formula. The calculation follows: x = [-4 ± √(4² - 4(1)(3))] / 2(1). The value under the square root (the discriminant) is 16 - 12, which simplifies to √4. Therefore, the square root of 4 is 2, leaving two possible solutions for x, based on adding or subtracting the square root.

### ✅ Finding the Two Solutions for x

In this final part, the presenter computes the two possible solutions for x. First, x = (-4 + 2) / 2, which simplifies to x = -1. Then, x = (-4 - 2) / 2, which gives x = -3. The two solutions are therefore x = -1 or x = -3, matching the result from the calculator. The step-by-step process concludes with the two answers verified manually.

### Mindmap

### Keywords

### 💡Quadratic Formula

### 💡Equation

### 💡Coefficients

### 💡Discriminant

### 💡Roots

### 💡Square Root

### 💡Plus or Minus (±)

### 💡Variable

### 💡Constant

### 💡Solution

### Highlights

Welcome and introduction to using the quadratic formula calculator.

Example problem: Solving x^2 + 4x + 3 = 0 using the calculator.

Typing the equation into the calculator and obtaining the result.

Calculator computes the solution: x = -1 or x = -3.

Explanation of solving the quadratic equation by hand.

Quadratic formula introduction: x = (-B ± sqrt(B^2 - 4AC)) / 2A.

Identifying coefficients A, B, and C from the equation.

Plugging the coefficients into the quadratic formula.

Detailed calculation under the square root: B^2 - 4AC.

Simplification of the expression under the square root.

Calculating the square root value.

Deriving two potential solutions from the quadratic formula.

Calculation of the first solution: x = -1.

Calculation of the second solution: x = -3.

Summary of solving quadratic equations both by calculator and manually.

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