3 Ways to Find the X

Table of contents:

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

Finding the x is often a student's introduction to algebra. Finding it means solving an equation to find out for which values of x it holds. There are very simple rules to follow to solve an equation correctly. Respecting the order of operations ensures that it is solved correctly. The x must be isolated in one member of the equation. When doing this you must remember to apply the same process to both members.

Steps

Method 1 of 3: Order of Operations

Step 1. Calculate everything in parentheses

To prove the order of operations we will use this equation: 2 ^ 2 (4 + 3) + 9-5 = x
2 ^ 2 (7) + 9-5 = x

Step 2. Calculate all powers

4 (7) + 9-5 = x

Step 3. Starting from left to right, perform all multiplications and divisions

28 + 9-5 = x

Step 4. Still going from left to right, add and subtract

Step 5. 37-5 = x

Step 6. 32 = x

Method 2 of 3: Isolating the x

Step 1. Solve the brackets

To demonstrate the isolation of x, we will use the example above by replacing a value at the first member with x and equating the equation to the value we calculated.
2 ^ 2 (x + 3) + 9-5 = 32
In this case we cannot resolve the parenthesis because it contains our variable x.

Step 2. Solve the exponents

4 (x + 3) + 9-5 = 32

Step 3. Solve the multiplication

4x + 12 + 9-5 = 32

Step 4. Solve addition and subtraction

4x + 21-5 = 32
4x + 16 = 32

Step 5. Subtract 16 from each side of the equation

The x must remain alone. To do this, we subtract 16 from the first member of the equation. Now you have to subtract the second member as well.
4x + 16-16 = 32-16
4x = 16

Step 6. Divide members by 4

4x / 4 = 16/4
x = 4

Method 3 of 3: Another example

Step 1. 2x ^ 2 + 12 = 44

Step 2. Subtract 12 from each member

2x ^ 2 + 12-12 = 44-12
2x ^ 2 = 32

Step 3. Divide each member by 2

(2x ^ 2) / 2 = 32/2
x ^ 2 = 16

Step 4. Calculate the square root of the members

x = 4

Advice

Radicals, or roots, are another way of representing powers. The square root of x = x ^ 1/2.
To verify the result, replace the x in the starting equation with the value you found.

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