How To Solve Quadratic Equations Using The Quadratic Formula

Summary

This video provides a step-by-step guide on how to solve quadratic equations using the quadratic formula. It demonstrates the process with two detailed examples, explaining how to identify the coefficients a, b, and c, substitute them into the formula, and simplify to find the solutions for x. The video also shows how to verify the answers.

Highlights

Introduction to the Quadratic Formula00:00:00

The video begins by introducing the quadratic formula as a method to solve quadratic equations of the form ax^2 + bx + c = 0. The formula itself is presented: x = [-b ± √(b^2 - 4ac)] / 2a.

First Example: Applying the Formula00:00:07

The first example used is 2x^2 + 3x - 2 = 0. The video explains how to identify a=2, b=3, and c=-2. These values are then substituted into the quadratic formula. The calculation proceeds by simplifying the expression under the square root and then splitting the equation into two parts due to the ± sign.

Simplifying and Finding Solutions (Example 1)00:01:15

After substitution, the expression simplifies to [-3 ± √(9 + 16)] / 4, which becomes [-3 ± √25] / 4. This further simplifies to (-3 ± 5) / 4, yielding two solutions: x = (2/4) = 1/2 and x = (-8/4) = -2. The video demonstrates how to check one of the solutions by plugging it back into the original equation.

Second Example: Another Application00:03:28

The second example is 6x^2 - 17x + 12 = 0. Here, a=6, b=-17, and c=12. These values are substituted into the quadratic formula. The calculation involves squaring -17 and multiplying -4ac.

Simplifying and Finding Solutions (Example 2)00:04:13

The expression inside the square root simplifies to 289 - 288 = 1. So, the formula becomes [17 ± √1] / 12, which is (17 ± 1) / 12. This leads to two solutions: x = (17+1)/12 = 18/12 = 3/2 and x = (17-1)/12 = 16/12 = 4/3. The video concludes by reiterating the successful application of the quadratic formula.