SOLUTION: solve the equation by completing the square. t^2-12t+20=0. how do i solve it?

Question 124353: solve the equation by completing the square. t^2-12t+20=0. how do i solve it?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
note: I'm going to use x instead of t

Start with the given equation

Subtract from both sides

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Now add to both sides to isolate y

Combine like terms

Now we're done with completing the square

Now to solve for x, let

Add to both sides

Reduce

Take the square root of both sides

Simplify the square root

Add to both sides

So the solution breaks down to

or

Combine like terms

or

So our answers are

or

Notice if we graph , we can see that the roots are and . So this visually verifies our answer.

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