Question

please help
solve using the square root property.
2x^2-4=-166

Answer 1

2x^2=-162
x^2=-81
x=-9

Answer 2

x=+and-9

Answer 3

Always check your answer for validity. In this case: 2(-9)^2 -4 = -166
2(81) - 4 = -166
162 - 4 = -166
158 = -166 Ooops It is not a -9, well lets check further is it the +9
2(9)^2 - 4 = -166
162 - 4 = -166
again 158 = -166 OOoops again. Neither is correct!! What went wrong???

Lets work this problem again
2x^2 - 4 = -166 Lets add 4 to both sides of the equal sign (a legal operation)

2x^2 = =-166 + 4 = -162
2x^2 = -162 Now lets divide both sides by 2.........another legal operation.
x^2 = -81 What now? Looks like all we need to do is take the square root of both sides. Not so fast...note the negative value on the right the -81.
Pay attention. There is no real number that when squared that will equal -81 !!

What is one to do to solve this ??? Use the imaginary number "i" That is the number when squared equals a -1, or i^2=-1, better yet i = the square root of -1. So the problem is now like this:

Answer 4

sqrt x^2 = sqrt -81
sqrt x^2 = sqrt [81 (-1)]
sqrt x^2 = sqrt [81 (i^2)]
x = 9i
Now lets validate (if possible) this answer
2x^2 -4 = -166 (the given problem)
2(9i)^2 - 4 = -166
(2)(81)(i^2) -4 = - 166 Now remember i^2 is a -1
(2)(81)(-1) - 4 = -166
162(-1) -4 = -166
-162 -4 = -166
-166 = -166

Leaving it up to you to prove that -9i is also an answer.

Answer 5

@jmedina163 @donmath do you understand?