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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
In general, there are three ways to solve quadratic equations:
  • Complete the square and find the square root fo each side.
  • Get one side equal to zero and
    • Factor; or
    • Use the Quadratic Formula
Most the the time completing the square is the most difficult. But when there is no x term, just x%5E2 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) x%5E2=60
The x terms are already on the left and x%5E2 is already a perfect square. So we will find the square root of each side:
sqrt%28x%5E2%29+=+sqrt%2860%29
A very common mistake is to think that sqrt%28x%5E2%29+=+x. It is not. sqrt%28x%5E2%29+=+abs%28x%29! So our equation simplifies to:
abs%28x%29+=+sqrt%2860%29
Solving an absolute value equation requires two equations:
x+=+sqrt%2860%29 or x = -sqrt%2860%29
Since sqrt%2860%29+=+sqrt%284%2A15%29+=+sqrt%284%29%2Asqrt%2815%29+=+2sqrt%2815%29 our final answer is
x+=+2sqrt%2815%29 or x+=+-2sqrt%2815%29

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) x%5E2-9=16
Add 9 to both sides
x%5E2+=+25
sqrt%28x%5E2%29+=++sqrt%2825%29
abs%28x%29+=+5
x+=+5 or x+=+-5

3) 4x%5E2%2B7=23
Subtract 7 from each side
4x%5E2+=+16
Divide both sides by 4
x%5E2+=+4
sqrt%28x%5E2%29+=+sqrt%284%29
abs%28x%29+=+2
x+-+2 or x+=+-2

4) x%5E2%2F6-2=0
Add 2 to both sides
x%5E2%2F6+=+2
Multiply both sides by 6
x%5E2+=+12
sqrt%28x%5E2%29+=+sqrt%2812%29
abs%28x%29+=+sqrt%2812%29
x+=+sqrt%2812%29 or x+=+-sqrt%2812%29
Since sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29+=+2sqrt%283%29
x+=+2sqrt%283%29 or x+=+-2sqrt%283%29