Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=−4+32,x2=4+32
Alternative Form
x1≈−2.871,x2≈2.871
Evaluate
x4−8x2−2
To find the roots of the expression,set the expression equal to 0
x4−8x2−2=0
Solve the equation using substitution t=x2
t2−8t−2=0
Substitute a=1,b=−8 and c=−2 into the quadratic formula t=2a−b±b2−4ac
t=28±(−8)2−4(−2)
Simplify the expression
More Steps
Evaluate
(−8)2−4(−2)
Multiply the numbers
More Steps
Evaluate
4(−2)
Multiplying or dividing an odd number of negative terms equals a negative
−4×2
Multiply the numbers
−8
(−8)2−(−8)
Rewrite the expression
82−(−8)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
82+8
Evaluate the power
64+8
Add the numbers
72
t=28±72
Simplify the radical expression
More Steps
Evaluate
72
Write the expression as a product where the root of one of the factors can be evaluated
36×2
Write the number in exponential form with the base of 6
62×2
The root of a product is equal to the product of the roots of each factor
62×2
Reduce the index of the radical and exponent with 2
62
t=28±62
Separate the equation into 2 possible cases
t=28+62t=28−62
Simplify the expression
More Steps
Evaluate
t=28+62
Divide the terms
More Steps
Evaluate
28+62
Rewrite the expression
22(4+32)
Reduce the fraction
4+32
t=4+32
t=4+32t=28−62
Simplify the expression
More Steps
Evaluate
t=28−62
Divide the terms
More Steps
Evaluate
28−62
Rewrite the expression
22(4−32)
Reduce the fraction
4−32
t=4−32
t=4+32t=4−32
Substitute back
x2=4+32x2=4−32
Solve the equation for x
More Steps
Substitute back
x2=4+32
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4+32
Separate the equation into 2 possible cases
x=4+32x=−4+32
x=4+32x=−4+32x2=4−32
Solve the equation for x
More Steps
Substitute back
x2=4−32
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4−32
Simplify the expression
More Steps
Evaluate
4−32
Evaluate the power
−4+32×−1
Evaluate the power
−4+32×i
x=±(−4+32×i)
Separate the equation into 2 possible cases
x=−4+32×ix=−−4+32×i
x=4+32x=−4+32x=−4+32×ix=−−4+32×i
Calculate
x=4+32x=−4+32
Solution
x1=−4+32,x2=4+32
Alternative Form
x1≈−2.871,x2≈2.871
Show Solution
