Solve each equation in Exercises 83–108 by the method of your choice. (3x - 4)^2 = 16

Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. They can be solved using various methods, including factoring, completing the square, or applying the quadratic formula. In the given equation, (3x - 4)^2 = 16, we recognize it as a quadratic equation that can be simplified to find the values of x.

Square Roots

Taking the square root is a fundamental operation in algebra that involves finding a number that, when multiplied by itself, gives the original number. In the context of the equation (3x - 4)^2 = 16, we can apply the square root to both sides to eliminate the square, leading to two possible equations: 3x - 4 = 4 and 3x - 4 = -4. This step is crucial for solving the equation.

Isolating Variables

Isolating variables is a key technique in algebra that involves rearranging an equation to solve for a specific variable. After applying the square root in the previous step, we will isolate x by performing algebraic operations such as addition, subtraction, multiplication, or division. This process allows us to find the values of x that satisfy the original equation.