SOLUTION: whats the answer to 7x rasied to the fourth plus 33x squared plus 6 equals 0?

Question 344616: whats the answer to 7x rasied to the fourth plus 33x squared plus 6 equals 0?
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
7x^(4)+33x^(2)+6=0 In this eqution ll of the"/" signs stand for +- and the "~" symbol refers to the square root.
Substitute u=x^(2) into the equation. This will make the quadratic formula easy to use.
7u^(2)+33u+6=0_u=x^(2)
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
7u^(2)+33u+6=0
Use the quadratic formula to find the solutions. In this case, the values are a=7, b=33, and c=6.
u=(-b\~(b^(2)-4ac))/(2a) where au^(2)+bu+c=0
Use the standard form of the equation to find a, b, and c for this quadratic.
a=7, b=33, and c=6
Substitute in the values of a=7, b=33, and c=6.
u=(-33\~((33)^(2)-4(7)(6)))/(2(7))
Simplify the section inside the radical.
u=(-33\~(921))/(2(7))
Simplify the denominator of the quadratic formula.
u=(-33\~(921))/(14)
First, solve the + portion of \.
u=(-33+~(921))/(14)
Next, solve the - portion of \.
u=(-33-~(921))/(14)
The final answer is the combination of both solutions.
u=(-33+~(921))/(14),(-33-~(921))/(14)
Substitute the real value of u=x^(2) back into the solved equation.
x^(2)=-0.19_x^(2)=-4.52
Solve the first equation for x.
x^(2)=-0.19
Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.
x=\~(-0.19)
Take the square root of -0.19 to get 0.44i.
x=\0.44i
First, substitute in the + portion of the \ to find the first solution.
x=0.44i
The complete solution is the result of both the + and - portions of the solution.
x=0.44i,0.44i
Solve the second equation for x.
x^(2)=-4.52
Solve the equation for x.
x=2.13i,-2.13i
The solution to 7x^(4)+33x^(2)+6=0 is x=0.44i,0.44i,2.13i,-2.13i.
x=0.44i,0.44i,2.13i,-2.13i
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