How To Solve Quadratic Equations By Completing The Square | Summary and Q&A

TL;DR

Learn how to solve quadratic equations by completing the square method with step-by-step instructions.

Key Insights

• ❎ Completing the square involves moving the constant term, adding the square of half the middle coefficient, factoring the trinomial, and taking the square root.
• ❓ Quadratic equations can have two possible solutions.
• ✅ Checking the answers by substituting them back into the original equation is necessary to verify their correctness.

Transcript

in this video we're going to talk about how to solve a quadratic equation by completing the square so the first thing we need to do is take the constant term negative 15 and move it from the left side to the right side of the equation now in order to do so the sign is going to change from negative 15 to positive 15. and we're going to have x square... Read More

Questions & Answers

Q: How do you begin solving a quadratic equation by completing the square?

To start, move the constant term to the other side of the equation and change its sign. Then, take half of the middle coefficient, square it, and add it to both sides of the equation.

Q: What is the shortcut for factoring the trinomial in completing the square?

The shortcut is to write "x" for the variable, write the sign in front of the middle term, and write the number before squaring it. The square goes on the outside. For example, "x^2 + x + 1" can be factored as "(x + 1)^2".

Q: How do you solve for x after completing the square?

After removing the square, isolate the variable "x" by moving the other terms to the other side of the equation. To find the two possible solutions, calculate the positive and negative values when solving for x.

Q: Why is it important to check the solutions?

Checking the answers by substituting them back into the original equation ensures that they are correct. If both sides of the equation are equal, then the solutions are valid.

Summary & Key Takeaways

• Move the constant term to the other side of the equation and change its sign.

• Take half of the middle coefficient, square it, and add it to both sides of the equation.

• Factor the trinomial on the left side using the shortcut "x + (sign)(number before squaring)".

• Take the square root of both sides to remove the square.

• Solve for x by isolating the variable and calculate the two possible solutions.

• Check the answers by substituting them back into the original equation.