Here are the essential concepts you must grasp in order to answer the question correctly.
Square Roots
Square roots are mathematical operations that determine a number which, when multiplied by itself, gives the original number. In the equation √(x+2) = 1 - √(3x+7), understanding how to manipulate square roots is essential for isolating variables and solving the equation. It is important to remember that squaring both sides of an equation can eliminate the square root but may introduce extraneous solutions.
Recommended video:
Imaginary Roots with the Square Root Property
Isolating Variables
Isolating variables is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable of interest on one side and all other terms on the opposite side. In the given equation, isolating the square root expressions will help simplify the problem and make it easier to solve for x.
Recommended video:
Equations with Two Variables
Extraneous Solutions
Extraneous solutions are solutions that emerge from the process of solving an equation but do not satisfy the original equation. When squaring both sides of an equation, it is crucial to check all potential solutions in the original equation to ensure they are valid. This concept is particularly relevant in equations involving square roots, as squaring can introduce solutions that are not applicable.
Recommended video:
Categorizing Linear Equations