How to Solve x^2 - 6x = 16

Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

This lesson will go over the steps to solve the equation x^2 - 6x = 16. We will examine two different solving processes, and learn how to check our work for accuracy.

Steps to Solve

We will look at two methods of solving x 2 - 6x = 16. The first uses factoring, and the second uses the quadratic formula.

Solving Using Factoring

When solving by factoring, we will use the following steps:

1.) Get all non-zero terms on one side of the equation, and zero on the other.

2.) Factor the non-zero side of the equation.

3.) Set each factor equal to zero and solve.

The first thing we want to do is get all non-zero terms on one side of the equation. To do this, we subtract 16 from both sides of the equation as shown.


The next step is to factor the non-zero side of the equation, so we want to factor x 2 - 6x - 16. When the coefficient in front of x 2 is one, as it is in our case, we can use the process shown in the image to factor.

How to Factor

We want to factor x 2 - 6x - 16, so we want to fill the blanks of (x + _____)(x + _____) with two numbers that when multiplied, are equal to -16 and when added, are equal to -6. We can find this by listing the numbers that multiply together to equal -16, and then check each one to see if they add up to -6.

Factors of 16 Sum
1 and -16 1 + (-16) = -15
-1 and 16 -1 + 16 = 15
2 and -8 2 + (-8) = -6
-2 and 8 -2 + 8 = 6
4 and -4 4 + (-4) = 0

The only pair of factors of 16 that add up to -6 are 2 and -8, so these are the numbers we will use to fill in the blanks. That is, x 2 - 6x - 16 = (x + 2)(x - 8).

The last step is to set each of these factors equal to zero and solve as shown.


We see that x = -2 or x = 8.

Solving Using the Quadratic Formula

Another way to solve this problem is using the quadratic formula. The quadratic formula gives solutions to an equation of the form ax 2 + bx + c = 0.

The Quadratic Formula

To solve using the quadratic formula, we use the following steps:

1.) Put the equation in the form ax 2 + bx + c = 0 by getting all non-zero terms on one side and zero on the other side.

2.) Identify the values of a, b, and c in your equation from step 1.

3.) Plug your values for a, b, and c into the quadratic formula and simplify.

In our example, we want to solve x 2 - 6x = 16. The first step is the same as the first step when we used factoring. We get all the non-zero terms on one side by subtracting 16 from both sides to get x 2 - 6x - 16 = 0.

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