Results for "x 2 −x−72"

The expression x^2 - x - 72 is a quadratic equation that can be factored or solved using various methods to find the values of x that satisfy it.

Introduction

The quadratic expression x^2 - x - 72 can be analyzed to find its roots, which are the values of x that make the equation equal to zero. Quadratic equations like this one are fundamental in algebra and can be solved using factoring, completing the square, or the quadratic formula. To solve x^2 - x - 72, we look for two numbers that multiply to -72 and add to -1. These numbers are 8 and -9, allowing us to factor the equation as (x - 9)(x + 8) = 0.

Understanding how to work with quadratic equations is essential for students and anyone dealing with algebra. Here are some key points to consider:
  • Quadratic equations are of the form ax^2 + bx + c.
  • They can have zero, one, or two real solutions.
  • Factoring is a common method for finding the roots.
  • The quadratic formula can also be used: x = (-b ± √(b² - 4ac)) / 2a.

This equation is a great example of how algebra can be applied to solve problems and understand relationships between variables. Whether you are a student or a professional, mastering quadratic equations like x^2 - x - 72 can enhance your mathematical skills and boost your confidence in tackling more complex problems.

FAQs

How can I factor the quadratic equation x^2 - x - 72?

To factor x^2 - x - 72, look for two numbers that multiply to -72 and add to -1. The numbers 8 and -9 work, so the factored form is (x - 9)(x + 8) = 0.

What are the solutions to the equation x^2 - x - 72?

The solutions to the equation x^2 - x - 72 can be found by setting each factor equal to zero. This gives x = 9 and x = -8.

What is the quadratic formula?

The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a, which can be used to find the roots of any quadratic equation.

Can all quadratic equations be factored?

Not all quadratic equations can be factored easily. Some may require the quadratic formula if they do not have rational roots.

What is the significance of the discriminant in a quadratic equation?

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation. If it's positive, there are two real solutions; if zero, one real solution; and if negative, no real solutions.