How to solve Quadratic Equations by Completing the Square

TL;DR

Learn how to use the completing the square method to solve quadratic equations in a few simple steps.

Transcript

good day welcome to the tech math Channel I'm Josh in this video we're going to look at how to use the completing and square method to solve quadratic equations so we'll start with a nice easy example we have x^2 - 6 x + 5 is equal to zero where what we're trying to do is solve for the values of X there so very first step what we do is we're going ... Read More

Key Insights

• ❎ The completing the square method simplifies quadratic equations by rewriting them in a perfect square form.
• ☺️ If the coefficient of x is not 1, additional steps are needed to solve the equation.
• 🙃 The quadratic equation is simplified by adding the square of half the coefficient of x to both sides.
• 🙃 The final step involves square rooting both sides of the equation to find the values of x.
• ❎ The completing the square method can be applied to more complex quadratic equations as well.
• 🆘 Through solving quadratic equations, the method helps in identifying the solutions for x.
• ❓ Solving quadratic equations relies on understanding the coefficients and manipulating the equation.

Questions & Answers

Q: How is the completing the square method used to solve quadratic equations?

The completing the square method involves rewriting the quadratic equation in a perfect square form and then solving for x. This is done by manipulating the equation to complete the square and simplifying it.

Q: What is the significance of the coefficient of x being 1?

When the coefficient of x is 1, the completing the square method can be applied directly. If the coefficient is not 1, extra steps are required to manipulate the equation and solve for x.

Q: How do you find the value to square when completing the square?

To find the value to square, divide the coefficient of x by 2 and square the result. This value is then added to one side of the equation to keep it balanced.

Q: What are the final steps in solving a quadratic equation using the completing the square method?

After simplifying the equation, it is set equal to zero. Then, square root both sides to find the value of x. Remember to consider both the positive and negative square root values.

Summary & Key Takeaways

• The video teaches how to solve quadratic equations using the completing the square method.

• The first step is to check if the coefficient of x is 1. If not, additional steps are needed.

• Group the x values together and simplify the equation to find the solutions for x.