Solving Quadratic Equations By Completing The Square

TL;DR

Learn how to solve quadratic equations by completing the square, including factoring, taking square roots, and rationalizing expressions.

Transcript

now in this lesson we're going to solve quadratic equations by completing the square so let's start with this one x squared plus 4x is equal to 5. so to complete the square take half of the number in front of x which is 2 half of 4 is 2 and square it so we're going to add 2 squared to both sides whatever you do to the left side you must also do to ... Read More

Key Insights

• ❎ Completing the square is a method for solving quadratic equations.
• 😑 Factoring the quadratic expression after completing the square helps simplify the equation.
• 🙃 Taking square roots of both sides allows for finding the solutions.
• 😑 Rationalizing expressions is necessary when dealing with square root denominators.

Questions & Answers

Q: What is the process of completing the square in solving quadratic equations?

To complete the square, take half of the coefficient of the x-term, square it, and add it to both sides of the equation. This allows you to factor the quadratic expression and solve for the variable.

Q: How do you factor a quadratic expression after completing the square?

After completing the square, the quadratic expression can be factored as (x + a)(x + a), where a is the number obtained by taking half of the x-term coefficient and squaring it.

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

The steps involve moving any constant terms to one side, factoring out the coefficient of the x-term, completing the square, factoring the quadratic expression, taking the square root, and solving for the variable.

Q: How do you rationalize expressions in completing the square?

To rationalize an expression, you multiply the numerator and denominator by the conjugate of the denominator. This eliminates any square roots in the denominator, allowing for simplified and rational expressions.

Summary & Key Takeaways

• In this lesson, the speaker teaches how to solve quadratic equations by completing the square.

• The process involves factoring, taking square roots, and rationalizing expressions.

• The examples given demonstrate step-by-step solutions for different quadratic equations.