SOLUTION: x^(2)=-75 where x is a real number, solve with the quadratic formula

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Question 1085503: x^(2)=-75 where x is a real number, solve with the quadratic formula
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B75=0
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a=1
b=0
c=75
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x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-0+%2B-+sqrt%28+0%5E2-4%2A1%2A75+%29%29%2F%282%2A1%29+
x+=+%280+%2B-+sqrt%28+-300+%29%29%2F%282%29+
Since the value under the square root is negative, there are no real roots to this equation only complex ones.

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is NO real solutions.


Because the square of a real number is always POSITIVE (non-negative) number.


But if you want to apply the quadratic formula, then first calculate the discriminant of the equivalent quadratic equation 

in standard form:

x%5E2+%2B+75 = 0.      ( ax%5E2+%2Bbx+%2B+c = 0 )


The discriminant is equal to 

d = b%5E2+-+4ac = 0%5E2+-4%2A1%2A75 = -300.


The disciminant is negative, which says that the equation HAS NO real solutions.


On solving quadratic equations see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
    - HOW TO solve quadratic equation by completing the square - Learning by examples
    - Solving quadratic equations without quadratic formula
    - Who is who in quadratic equations

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".