SOLUTION: finding square roots 1) x^2=60 2) x^2-9=16 3) 4x^2+7=23 4) x^2/6-2=0

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Question 241004: finding square roots
1) x^2=60
2) x^2-9=16
3) 4x^2+7=23
4) x^2/6-2=0
Found 2 solutions by nyc_function, jsmallt9:
Answer by nyc_function(2741)   (Show Source): You can put this solution on YOUR website!
Post one question at a time or else your questions will be ignored by the tutors here.
I will do number one.
x^2 = 60
Take square root of both sides.
sqrt{x^2} = sqrt{60}
x = ± sqrt{4} times sqrt{15}
x = ± 2(sqrt{15})




Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
In general, there are three ways to solve quadratic equations:Most the the time completing the square is the most difficult. But when there is no x term, just terms, then completing the square is fairly easy. Since all of your problems have no x terms, we will complete the square.

To complete the square, get the x terms on one side and form a perfect square. Then find the square root of each side and solve.

1)
The x terms are already on the left and is already a perfect square. So we will find the square root of each side:

A very common mistake is to think that . It is not. ! So our equation simplifies to:

Solving an absolute value equation requires two equations:
or x =
Since our final answer is
or

On the remainder of the problems I will be using the same steps:
  1. Complete the square
    1. Gather the x terms on one side
    2. Form a perfect square
  2. Find the square root of each side
  3. Solve
So there will be fewer comments on the rest of the problems.

2)
Add 9 to both sides



or

3)
Subtract 7 from each side

Divide both sides by 4



or

4)
Add 2 to both sides

Multiply both sides by 6



or
Since
or

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