Solve each equation. See Examples 4–6. √3x=√(5x+1)-1

Key Concepts

Square Roots

Square roots are the values that, when multiplied by themselves, yield the original number. In the equation √3x, the square root indicates that we are looking for a number that, when squared, equals 3x. Understanding how to manipulate square roots is essential for solving equations involving them.

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, allowing for easier computation. In the given equation, isolating x will help in finding its value by simplifying the expression step by step.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax² + bx + c = 0, where a, b, and c are constants. When manipulating equations that involve square roots, it may lead to a quadratic form, requiring knowledge of how to solve such equations using factoring, completing the square, or the quadratic formula.