(2x+7)(x-1)=0 In Standard Form

3 min read Jun 16, 2024

Solving Quadratic Equations: From Factored Form to Standard Form

This article explores how to transform a quadratic equation from factored form to standard form. We'll use the example of (2x+7)(x-1)=0 to demonstrate the process.

Understanding the Factored Form

The equation (2x+7)(x-1)=0 is presented in factored form. This means the equation is expressed as a product of linear factors. Each factor represents a potential solution to the equation.

Finding the Solutions (Roots)

To find the solutions of the equation, we can use the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Therefore, we set each factor equal to zero and solve for x:

2x + 7 = 0
- 2x = -7
- x = -7/2
x - 1 = 0
- x = 1

This tells us the solutions to the equation are x = -7/2 and x = 1.

Transforming to Standard Form

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants. To convert our factored form equation to standard form, we need to expand the product:

Expand the product: (2x + 7)(x - 1) = 2x² - 2x + 7x - 7
Simplify by combining like terms: 2x² + 5x - 7 = 0

Therefore, the standard form of the quadratic equation (2x+7)(x-1)=0 is 2x² + 5x - 7 = 0.

Summary

By understanding factored form and the Zero Product Property, we can easily find the solutions of a quadratic equation. Additionally, we can transform the equation from factored form to standard form using simple algebraic manipulation. This process is essential for further analysis and solving quadratic equations using various techniques.