What you need to know

Things to remember:

  • We can find the value(s) that satisfy an equation by rearranging to get the variable by itself.

We have seen linear equations before, they’re equations that can be drawn as a straight line (they don’t have powers). So, they usually look something like this:

y=5x+2

y=7-3x

8y+5x=3

A nonlinear equation, however, cannot be drawn as a straight line. These equations involve powers and multiplying variables together. They look something like this:

y=x^2+4

y=\sqrt{x}

xy=8

We’re going to look at two types of questions here, and each will take two steps.

Solve the following nonlinear equation x^2+4=29.

 

Step 1: Get the variable by itself.

Hint: Remember, if we see an addition we subtract it, and if we see plus we subtract it.

 

x^2+4=29

x^2+4-4=29-4

x^2=25

 

Step 2: Do the opposite of what you’re doing to the x.

Hint: What is the opposite of square? Square rooting!

 

x^2=25

\sqrt{x^2}=\sqrt{25}

x=5

Note: A square root provides two answers, a positive and a negative (-5\times-5=25.

 

Solve the following nonlinear equation \sqrt{x}-3=9.

 

Step 1: Get the variable by itself.

Hint: Remember, if we see an addition we subtract it, and if we see plus we subtract it.

 

\sqrt{x}-3=9

\sqrt{x}+3=9+3

\sqrt{x}=12

 

Step 2: Do the opposite of what you’re doing to the x.

Hint: What is the opposite of square rooting? Squaring!

 

\sqrt{x}=12

\sqrt{x}^2=12^2

x=144

Example Questions

Step 1: Get the variable by itself.

 

Hint: Remember, if we see an addition we subtract it, and if we see plus we subtract it.

 

 

x^2-3=13

 

x^2+3=13 +3

 

x^2=16

 

 

Step 2: Do the opposite of what you’re doing to the x.

 

Hint: What is the opposite of square? Square rooting!

 

 

x^2=16

 

\sqrt{x^2}=\sqrt{16}

 

x=4

 

 

Note: A square root provides two answers, a positive and a negative (-4\times-4=16.)

Step 1: Get the variable by itself.

 

Hint: Remember, if we see an addition we subtract it, and if we see plus we subtract it.

 

 

\sqrt{x}+8=28

 

\sqrt{x}+8-8=28-8

 

\sqrt{x}=20

 

 

Step 2: Do the opposite of what you’re doing to the x.

 

Hint: What is the opposite of square rooting? Squaring!

 

 

\sqrt{x}=20

 

\sqrt{x}^2=20^2

 

x=400

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