Solve: x(2 x+9)=5

Name: Problem 97, Chapter 7: Introductory Algebra for College Students
Uploaded: 2021-02-19T05:06:33-08:00
Duration: 3 min 21 s
Channel: Matthew Biollo
Description: Solve: x(2 x+9)=5

Key Concepts

Quadratic Equations

A quadratic equation is an equation that can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. This concept is crucial in algebra as it encompasses finding the roots, understanding parabolic graphs, and applying solution techniques like factoring, completing the square, or using the quadratic formula.

Distributive Property

The distributive property allows you to multiply a single term by terms inside a parenthesis and is fundamental in expanding expressions. It simplifies the process of rearranging and simplifying equations, which is important when preparing a problem for further solution methods.

Rearranging Equations

Rearranging equations involves moving all terms to one side of the equation to set it equal to zero. This process is essential because it transforms the equation into a standard form, making it easier to apply methods like factoring or the quadratic formula to solve for the unknown variable.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac))/(2a), provides a universal method for solving quadratic equations once they are arranged in the standard form ax² + bx + c = 0. It is particularly useful when the equation does not factor easily, as it directly computes the roots using the coefficients.

Discriminant

The discriminant, given by b² - 4ac in the context of the quadratic formula, determines the nature of the roots of a quadratic equation. A positive discriminant indicates two distinct real roots, zero indicates a repeated real root, and a negative discriminant indicates complex roots.

Transcript

00:01 This problem deals with solving what looks like an equation, but really we will be just factoring a trinomial in the end.

00:09 So first thing we want to do with this is to distribute the x within the group, and what you'll get then is x times 2x will give you 2x squared.

00:20 X times positive 9 is plus 9x, and that's all equal to 5.

00:27 Now let's bring the 5 over to the other side, by subtracting 5, but what i do to one side, i have to do to both sides.

00:34 And here is my trinomial that i'm going to have to end up factoring 2x squared plus 9x, subtract 5.

00:42 So when you have a non -1 coefficient in front of your leading variable x squared there, we need to use a strategy where we're looking at, we're going to multiply 2 and negative 5.

00:56 So 2 multiplied by negative 5 gives you negative 10.

01:01 So now what i'm going to look to do is split up 9x into two numbers that will add to give us 9x, but multiply to give you negative 10.

01:17 So those numbers are going to be positive 10 times negative 1, because those add up to give you positive 9.

01:27 But multiply to give you negative 10.

01:30 So let's split up that 9x in that way.

01:34 So this becomes 2x squared plus 10x minus 1x, subtract 5 equals 0.

01:44 So now we can group each of these and factor those separately.

01:51 So 2x squared plus 10x, i can take out a 2x.

01:54 I'd be left with x plus 5.

02:00 And on this one, i can take out a negative 1, and you're left with x plus 5...