For What Values Of X Is X2 + 2x = 24 True?

When solving equations, it is important to know the values of the variables that will make the equation true. In this article, we will discuss the values of x that make the equation x2 + 2x = 24 true.

Solving the Equation

The first step in solving this equation is to isolate the variable, x. To do this, we need to subtract 2x from both sides of the equation. This will leave us with x2 = 24 – 2x.

Now, we can divide both sides of the equation by x. This leaves us with x = 24 – 2x, which can be rearranged to give us x = 12.

Finding the Value of X

Now that we have solved the equation, we can determine the value of x. In this case, the value of x is 12. This means that when x2 + 2x = 24, the value of x must be 12.

In conclusion, the equation x2 + 2x = 24 is true when the value of x is 12. It is important to remember that when solving equations, it is necessary to isolate the variable to determine its value.

Generally accepted standard mathematical notation can improve the understanding of any given problem. This article aims to explain the values of x for which the equation x² + 2x = 24 is true.

The equation in question is in what is known as a quadratic form, where the highest exponent of x is 2. This type of equation can sometimes be solved by the simple application of basic algebraic principles, and other times (such as in this case) with a method called ‘completing the square.’

The goal of solving this equation is to isolate one side of the equation until a numerical coefficient is obtained. It turns out that this particular equation can be solved algebraically without completion of the square. Essentially, we need to solve for the part of the equation involving x on one side and the constant 24 on the other.

Subtract 24 from both sides of the equation and then add the coefficient of x² to both sides to give us the equation x² + 6x + 18 = 0.We can then use a mathematical skill known as ‘factoring’. Factoring is the technique of breaking a number or expression down into two or more related integers. By applying the technique of factoring, the equation can be rewritten as (x + 9)(x+2) = 0.

Now, by observing both factors, we can figure out that when x = -9 or x = -2 the equation will be true. Therefore we can conclude that x must be equal to either -2 or -9 in order for x² + 2x = 24 to be true.

In summary, the values of x for which the equation x² + 2x = 24 is true are -2 and -9. This demonstrates the usefulness of basic algebraic principles, as well as the mathematical tool of factoring, in solving quadratic equations.