(4x-1)(4x-1)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (4x-1)(4x-1) = 0

This equation represents a simple quadratic equation in factored form. Let's break down how to solve it.

Understanding the Equation

The equation (4x-1)(4x-1) = 0 is already factored, which means it's written as a product of two expressions. For the product of two expressions to equal zero, at least one of them must be zero.

Solving for x

1. Set each factor equal to zero:

   • 4x - 1 = 0

2. Solve for x in each equation:

   • 4x = 1
   • x = 1/4

Solution

Since both factors are the same (4x-1), we get the same solution twice. Therefore, the solution to the equation (4x-1)(4x-1) = 0 is x = 1/4.

Key Concepts

• Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.
• Factoring: Writing an expression as a product of simpler expressions.
• Quadratic Equation: An equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

By understanding these concepts, we can solve quadratic equations in factored form efficiently.