Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Intro to Quadratic Equations

College Algebra

1. Equations & Inequalities

Intro to Quadratic Equations

Previous problemNext problem

1:32 minutes

Problem 103

Textbook Question

Solve each equation in Exercises 83–108 by the method of your choice.2x^2 - 7x = 0

Verified step by step guidance

First, notice that the equation is a quadratic equation in the form of \( ax^2 + bx + c = 0 \). Here, \( a = 2 \), \( b = -7 \), and \( c = 0 \).

Since the equation is set to zero, we can factor it. Start by factoring out the greatest common factor from the terms on the left side. The greatest common factor of \( 2x^2 \) and \( -7x \) is \( x \).

Factor \( x \) out of the equation: \( x(2x - 7) = 0 \).

Now, apply the zero product property, which states that if a product of factors equals zero, at least one of the factors must be zero. Set each factor equal to zero: \( x = 0 \) and \( 2x - 7 = 0 \).

Solve each equation separately. The first equation is already solved: \( x = 0 \). For the second equation, solve for \( x \) by adding 7 to both sides and then dividing by 2: \( 2x = 7 \) becomes \( x = \frac{7}{2} \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Factoring Quadratic Equations

Factoring is a method used to solve quadratic equations by expressing them as a product of their linear factors. In the equation 2x^2 - 7x = 0, we can factor out the common term, which simplifies the equation and allows us to find the values of x that satisfy it.

Zero Product Property

The Zero Product Property states that if the product of two factors equals zero, at least one of the factors must be zero. This principle is crucial when solving factored equations, as it allows us to set each factor equal to zero to find the solutions for the variable.

Quadratic Formula

The Quadratic Formula, x = (-b ± √(b² - 4ac)) / (2a), provides a method for solving any quadratic equation of the form ax² + bx + c = 0. While not necessary for this specific problem, it is a valuable tool for finding solutions when factoring is not straightforward or possible.