SOLUTION: Find all real soultions. x^2+30x + 200 = 0 x^2 + 3x + 1 = 0 X^2- 6x + 1 = 0 3x^2 + 7x + 4 = 0

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Question 295330: Find all real soultions.
x^2+30x + 200 = 0
x^2 + 3x + 1 = 0
X^2- 6x + 1 = 0
3x^2 + 7x + 4 = 0
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
# 1

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=30, and c=200




Square 30 to get 900




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


or


Lets look at the first part:





Add the terms in the numerator

Divide


So one answer is






Now lets look at the second part:





Subtract the terms in the numerator

Divide


So another answer is




So our solutions are:

or




======================
# 2

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=3, and c=1




Square 3 to get 9




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


or



Now break up the fraction



or



Simplify



or



So the solutions are:

or






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