Question 346914: How do I solve this quadratic equation?
w^4-14w^2-2=0
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! w^(4)-14w^(2)-2=0
NOTE: ANY / SYMBOLS STAND FOR THE +- SIGN AND THE ~ SIGN STANDS FOR THE SQUARE ROOT SYMBOL.
Substitute u=w^(2) into the equation. This will make the quadratic formula easy to use.
u^(2)-14u-2=0_u=w^(2)
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
u^(2)-14u-2=0
Use the quadratic formula to find the solutions. In this case, the values are a=1, b=-14, and c=-2.
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=1, b=-14, and c=-2
Substitute in the values of a=1, b=-14, and c=-2.
u=(-(-14)\~((-14)^(2)-4(1)(-2)))/(2(1))
Multiply -1 by each term inside the parentheses.
u=(14\~((-14)^(2)-4(1)(-2)))/(2(1))
Simplify the section inside the radical.
u=(14\2~(51))/(2(1))
Simplify the denominator of the quadratic formula.
u=(14\2~(51))/(2)
First, solve the + portion of \.
u=(14+2~(51))/(2)
Simplify the expression to solve for the + portion of the \.
u=7+~(51)
Next, solve the - portion of \.
u=(14-2~(51))/(2)
Simplify the expression to solve for the - portion of the \.
u=7-~(51)
The final answer is the combination of both solutions.
u=7+~(51),7-~(51)
Substitute the real value of u=w^(2) back into the solved equation.
w^(2)=14.14_w^(2)=-0.14
Solve the first equation for w.
w^(2)=14.14
Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.
w=\~(14.14)
Take the square root of 14.14 to get 3.76.
w=\3.76
First, substitute in the + portion of the \ to find the first solution.
w=3.76
Next, substitute in the - portion of the \ to find the second solution.
w=-3.76
The complete solution is the result of both the + and - portions of the solution.
w=3.76,-3.76
Solve the second equation for w.
w^(2)=-0.14
Solve the equation for w.
w=0.38i,0.38i
The solution to w^(4)-14w^(2)-2=0 is w=3.76,-3.76,0.38i,0.38i.
w=3.76,-3.76,0.38i,0.38i
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