Unit 1:The square root method!

This is an example of a problem, following the sqaure root method.

Step 1:-2x^2+24=x^2-3

My first step is writing my original equation. My goal is to solve this equation using the Square Root Method. I will have to solve it and simplify it, until the x is by itself. At the end I should have two possible answers for the value of x.

Step 2: -2x^2+24-24=x^2-3-24

My next step is to get the -2x^2 by itself by removing the number that is not attached the the x. This can be removed by subtraction, so I then subtract 24 from both sides. When I subtract 24 from positive 24 they cancel out, so then I move to the other side and subract 24 from negative 3 which leaves me with -27. This is due to the negative to a negative rule which states that when you subtract a number from a negative number you add them and keep the sign.

Step 3: -2x^2= x^2-27

The next minor step is to cancel out the numbers that can be cancelled out and then rewrite the new equation to keep yourself organized.

Step 4: -2x^2-x^2= x^2-x^2-27

My next step is to subtract x^2 from both sides in order to have x by itself and set to a number. So when you subtract x^2 from itself they cancel out and leave you with -27 on one side and then when you subtract x^2 from -2x^2 and you are left with -3x^2.

Step 5: -3x^2= -27

This is the new equation that you write out after completing the steps above. After rewriting this equation you proceed to finding the solution by dividing both sides by -3. This will allow you to get the x2 by itself on one side. When you divide -3x^2 by -3 you are left with x^2. It is a rule when solving an equation to always do what you do on one side to the other, so you then have to divide the -27 by -3, which leaves you with 9.

Step 6: x^2=9

This is what you get once you divide both sides by -3. From this point, you have to take the sqaure root of each side in order to get the x by itself. When you take the square root of x^2 the raidical sign and the square cancel eachother out and then you are left with x=9.When you get this you then have to solve for the square root of 9, which leaves you with 3. This brings you to your final solution which is that x=±3.