Solving an Equation with Two Square Roots || Example with Quadratics Inside the Roots

TL;DR

This video explores the step-by-step process of solving an equation with two square roots using squaring and factoring techniques.

Transcript

hello in this video we're going to solve an equation with two square roots we have the square root of x squared plus 5x minus 6 plus the square root of x squared plus 3x minus 3 and it's all equal to 1. let's go ahead and carefully work through this solution the first step is going to be to isolate one of the square roots that we can eliminate it b... Read More

Key Insights

• 🫚 Solving equations with two square roots involves isolating and eliminating one of the square roots by subtraction and squaring.
• ❎ The formula for simplifying the remaining square root is derived from expanding the square of a difference between two terms.
• 🍉 Factoring can be used to combine like terms and manipulate the equation to solve for x.

Questions & Answers

Q: How is the initial step of isolating one of the square roots achieved?

The process involves subtracting one square root term from both sides of the equation to have a single square root on one side, allowing for its elimination through squaring.

Q: What is the formula used to simplify the remaining square root?

The formula used is "a minus b" squared, where a represents the first term and b represents the second term. By applying this formula, the second square root is expanded and simplified.

Q: How is the equation further manipulated to solve for x?

The equation is rearranged by combining like terms on the right-hand side, canceling out some terms on the left-hand side, and isolating the remaining square root. Subtraction and addition operations are then performed, resulting in a simplified equation for x.

Q: Why is it important to check the solution obtained?

Checking the solution is crucial to verify if it satisfies the original equation. Sometimes, solutions can be extraneous, meaning the obtained value does not actually fulfill the equation. In this case, plugging the solution back into the original equation confirms its validity.

Summary & Key Takeaways

• The video demonstrates how to isolate one of the square roots by subtracting it from both sides of the equation.

• The equation is squared on both sides, resulting in the elimination of the square root on one side and the use of a formula to simplify the other square root.

• By combining like terms and isolating the remaining square root, the equation is further manipulated and solved for x.