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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (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


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B30%2Ax%2B200=0 ( notice a=1, b=30, and c=200)





x+=+%28-30+%2B-+sqrt%28+%2830%29%5E2-4%2A1%2A200+%29%29%2F%282%2A1%29 Plug in a=1, b=30, and c=200




x+=+%28-30+%2B-+sqrt%28+900-4%2A1%2A200+%29%29%2F%282%2A1%29 Square 30 to get 900




x+=+%28-30+%2B-+sqrt%28+900%2B-800+%29%29%2F%282%2A1%29 Multiply -4%2A200%2A1 to get -800




x+=+%28-30+%2B-+sqrt%28+100+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-30+%2B-+10%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-30+%2B-+10%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-30+%2B+10%29%2F2 or x+=+%28-30+-+10%29%2F2


Lets look at the first part:


x=%28-30+%2B+10%29%2F2


x=-20%2F2 Add the terms in the numerator

x=-10 Divide


So one answer is

x=-10




Now lets look at the second part:


x=%28-30+-+10%29%2F2


x=-40%2F2 Subtract the terms in the numerator

x=-20 Divide


So another answer is

x=-20


So our solutions are:

x=-10 or x=-20




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# 2

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


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B3%2Ax%2B1=0 ( notice a=1, b=3, and c=1)





x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 Plug in a=1, b=3, and c=1




x+=+%28-3+%2B-+sqrt%28+9-4%2A1%2A1+%29%29%2F%282%2A1%29 Square 3 to get 9




x+=+%28-3+%2B-+sqrt%28+9%2B-4+%29%29%2F%282%2A1%29 Multiply -4%2A1%2A1 to get -4




x+=+%28-3+%2B-+sqrt%28+5+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-3+%2B-+sqrt%285%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-3+%2B-+sqrt%285%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-3+%2B+sqrt%285%29%29%2F2 or x+=+%28-3+-+sqrt%285%29%29%2F2



Now break up the fraction



x=-3%2F2%2Bsqrt%285%29%2F2 or x=-3%2F2-sqrt%285%29%2F2



Simplify



x=-3%2F2%2Bsqrt%285%29%2F2 or x=-3%2F2-sqrt%285%29%2F2



So the solutions are:

x=-3%2F2%2Bsqrt%285%29%2F2 or x=-3%2F2-sqrt%285%29%2F2