Algebra 75  Completing the Square  part 1  Summary and Q&A
TL;DR
Completing the square is a technique used to solve any quadratic equation by transforming the quadratic expression into a perfect square and then solving for the variable.
Key Insights
 π» Completing the square is a method that allows for solving any quadratic equation, even if it cannot be factored.
 π By transforming the equation into a perfect square expression, it becomes easier to solve.
 π The constant term used to complete the square is determined by taking half of the coefficient of the xterm and squaring it.
 β Geometrically, completing the square can be visualized as adding a square with sides of length "b over two" to represent the constant term.
 βΊοΈ Completing the square can also be used to find the xintercepts of quadratic functions that cannot be factored.
 βΊοΈ The technique is applicable when the coefficient of the xsquared term is 1.
 β Completing the square involves manipulating the equation to isolate the squared linear expression and then solving for the variable by taking the square root.
Transcript
Hello. I'm Professor Von Schmohawk and welcome to Why U. So far, we have seen that quadratic equations can be solved if we can factor the quadratic expression into a pair of linear expressions. However, there are many quadratics that are not practical or even possible to factor using any of the methods we have presented so far. Over one thousand ye... Read More
Questions & Answers
Q: What is completing the square?
Completing the square is a technique used to solve quadratic equations that cannot be easily factored. It involves transforming the quadratic equation into an equation with a perfect square quadratic expression.
Q: How does completing the square work?
Completing the square works by adding or subtracting a constant term to the quadratic equation to make it a perfect square. This constant term is determined by taking half of the coefficient of the xterm, squaring it, and adding it to the equation.
Q: Can all quadratic equations be solved using completing the square?
Yes, completing the square can be used to solve any quadratic equation, even those that cannot be factored using traditional methods.
Q: What are the steps to complete the square?
The steps for completing the square are: 1) Make sure the coefficient of the xsquared term is 1. 2) Move the constant term to the right side of the equation. 3) Add the squared value of half of the coefficient of the xterm to both sides of the equation. 4) Write the left side as a perfect square and simplify the right side. 5) Take the square root of both sides and solve for the variable.
Summary & Key Takeaways

Completing the square is a method for solving quadratic equations that cannot be factored easily.

It involves transforming a quadratic equation into an equation with a perfect square quadratic expression.

By taking the square root of both sides, the equation can be simplified and solved for the variable.