Solve each equation. See Examples 4–6. √(4x+13) = 2x-1

Key Concepts

Square Roots

Square roots are the values that, when multiplied by themselves, yield the original number. In the equation √(4x + 13) = 2x - 1, understanding how to manipulate square roots is essential. This includes knowing that squaring both sides of the equation can eliminate the square root, leading to a polynomial equation that can be solved.

Isolating Variables

Isolating variables involves rearranging an equation to solve for a specific variable. In this case, after squaring both sides, you will need to collect all terms involving x on one side of the equation. This process is crucial for simplifying the equation and making it easier to solve for x.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax² + bx + c = 0. After manipulating the original equation, you may end up with a quadratic equation that can be solved using factoring, completing the square, or the quadratic formula. Recognizing the form of a quadratic equation is vital for finding the solutions to the problem.