Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=−21+2,x2=21+2
Alternative Form
x1≈−3.107548,x2≈3.107548
Evaluate
x4−8x2−16
To find the roots of the expression,set the expression equal to 0
x4−8x2−16=0
Solve the equation using substitution t=x2
t2−8t−16=0
Substitute a=1,b=−8 and c=−16 into the quadratic formula t=2a−b±b2−4ac
t=28±(−8)2−4(−16)
Simplify the expression
More Steps
Evaluate
(−8)2−4(−16)
Multiply the numbers
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Evaluate
4(−16)
Multiplying or dividing an odd number of negative terms equals a negative
−4×16
Multiply the numbers
−64
(−8)2−(−64)
Rewrite the expression
82−(−64)
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+64
Evaluate the power
64+64
Add the numbers
128
t=28±128
Simplify the radical expression
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Evaluate
128
Write the expression as a product where the root of one of the factors can be evaluated
64×2
Write the number in exponential form with the base of 8
82×2
The root of a product is equal to the product of the roots of each factor
82×2
Reduce the index of the radical and exponent with 2
82
t=28±82
Separate the equation into 2 possible cases
t=28+82t=28−82
Simplify the expression
More Steps
Evaluate
t=28+82
Divide the terms
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Evaluate
28+82
Rewrite the expression
22(4+42)
Reduce the fraction
4+42
t=4+42
t=4+42t=28−82
Simplify the expression
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Evaluate
t=28−82
Divide the terms
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Evaluate
28−82
Rewrite the expression
22(4−42)
Reduce the fraction
4−42
t=4−42
t=4+42t=4−42
Substitute back
x2=4+42x2=4−42
Solve the equation for x
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Substitute back
x2=4+42
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4+42
Simplify the expression
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Evaluate
4+42
Factor the expression
4(1+2)
The root of a product is equal to the product of the roots of each factor
4×1+2
Evaluate the root
21+2
x=±21+2
Separate the equation into 2 possible cases
x=21+2x=−21+2
x=21+2x=−21+2x2=4−42
Solve the equation for x
More Steps
Substitute back
x2=4−42
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4−42
Simplify the expression
More Steps
Evaluate
4−42
Evaluate the power
−4+42×−1
Evaluate the power
−4+42×i
Evaluate the power
2−1+2×i
x=±(2−1+2×i)
Separate the equation into 2 possible cases
x=2−1+2×ix=−2−1+2×i
x=21+2x=−21+2x=2−1+2×ix=−2−1+2×i
Calculate
x=21+2x=−21+2
Solution
x1=−21+2,x2=21+2
Alternative Form
x1≈−3.107548,x2≈3.107548
Show Solution
