Solve 5x^2 - 75x - 30 = 0 by Completing the Square MyMathlab Homework

TL;DR

This video explains how to solve a quadratic equation by completing the square, using a step-by-step approach.

Transcript

in this video we have to solve a quadratic equation by completing the square so we have 5x squared minus 75 X minus 30 equals zero so before we complete the square it's really important that the coefficient of x squared is 1 so we'll start by dividing everything by 5 when we do that we end up with x squared 75 over 5 is 15 and then 30 over 5 is 6 a... Read More

Key Insights

• 🗂️ Dividing the equation by the coefficient of the x-squared term normalizes it for completing the square.
• ❎ Adding a square term to both sides of the equation transforms it into a perfect square trinomial.
• 🫱 Simplifying the right-hand side of the equation by combining fractions ensures accurate solutions.
• ❎ Using the square root property allows us to find both positive and negative solutions.
• ❓ The process involves multiple steps, including factoring and simplifying fractions, to arrive at the final solutions.
• 🗂️ The video emphasizes the importance of consistently dividing the coefficient of x by 2 and squaring it.
• ❎ Completing the square can be a challenging method for solving quadratic equations but provides exact solutions.

Questions & Answers

Q: Why is it important to ensure that the coefficient of x-squared is 1 before completing the square?

When the coefficient is 1, it simplifies the process and makes it easier to find the solutions by completing the square. Dividing the equation by the coefficient helps to achieve this.

Q: How do you transform a quadratic equation into a perfect square trinomial?

By taking half of the coefficient of x, squaring it, and adding that value to both sides of the equation. This creates a square term that, when factored, results in a perfect square trinomial.

Q: What is the significance of adding fractions and simplifying the right-hand side of the equation?

Adding fractions on the right-hand side allows for simplification and ultimately finding the precise value of the constant term. It ensures that the solution is accurate.

Q: Why do we take the square root of both sides and use the square root property to find the solutions?

The square root property states that if two numbers have the same square, their values must be the positive and negative square roots of that number. By applying this property, we can determine the solutions of the quadratic equation.

Summary & Key Takeaways

• The video discusses the process of solving a quadratic equation by completing the square.

• The coefficient of the x-squared term is first normalized by dividing the equation by the coefficient.

• The equation is then rearranged to have only x-terms on one side, and a constant on the other side.

• The quadratic form is transformed into a perfect square trinomial by adding a square term to both sides.

• The right-hand side of the equation is simplified by combining fractions, if necessary.

• The equation is then factored, divided by the coefficient of x, and the square root property is applied to find the solutions.