Completing the square for quadratic formula | Quadratic equations | Algebra I | Khan Academy

TL;DR

The video explains how to complete the square and derive the quadratic formula to solve any quadratic equation.

Transcript

Complete the square on the general quadratic equation. We have ax squared plus bx plus c is equal to 0. So whenever I complete the square, actually whenever I deal with any of these types of quadratic equations, I always like to not have an a, or a non 1 coefficient, on the x squared terms. So let's make it into a 1 coefficient. And the easiest way... Read More

Key Insights

• ❎ Completing the square involves manipulating a quadratic equation to make the first three terms a perfect square trinomial.
• ❎ The quadratic formula is derived by isolating the squared binomial and solving for x.
• ❓ The quadratic formula can give two possible solutions for a quadratic equation.

Questions & Answers

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

Completing the square allows us to rewrite a quadratic equation as a perfect square trinomial, making it easier to solve.

Q: How is the quadratic formula derived?

The quadratic formula is derived by isolating the squared binomial, taking the square root of both sides, and solving for x.

Q: What if the square root part of the quadratic formula is negative?

If the square root is negative, it means that the quadratic equation has no real solutions.

Q: Can the quadratic formula be used to solve any type of quadratic equation?

Yes, the quadratic formula can be used to solve any quadratic equation, regardless of the values of a, b, and c.

Summary & Key Takeaways

• The first step in completing the square is to make the coefficient of the x-squared term 1 by dividing each term by a.

• By taking half of the coefficient of the x term, squaring it, and adding it to the equation, the first three terms become a perfect square trinomial.

• The quadratic formula is derived by isolating the squared binomial, taking the square root of both sides, and solving for x.