Question
Simplify the expression
−3x4−1
Evaluate
x4−2x3×2x−1
Multiply
More Steps

Multiply the terms
−2x3×2x
Multiply the terms
−4x3×x
Multiply the terms with the same base by adding their exponents
−4x3+1
Add the numbers
−4x4
x4−4x4−1
Solution
More Steps

Evaluate
x4−4x4
Collect like terms by calculating the sum or difference of their coefficients
(1−4)x4
Subtract the numbers
−3x4
−3x4−1
Show Solution

Find the roots
x1=−64108+64108i,x2=64108−64108i
Alternative Form
x1≈−0.537285+0.537285i,x2≈0.537285−0.537285i
Evaluate
x4−2x3×2x−1
To find the roots of the expression,set the expression equal to 0
x4−2x3×2x−1=0
Multiply
More Steps

Multiply the terms
2x3×2x
Multiply the terms
4x3×x
Multiply the terms with the same base by adding their exponents
4x3+1
Add the numbers
4x4
x4−4x4−1=0
Subtract the terms
More Steps

Simplify
x4−4x4
Collect like terms by calculating the sum or difference of their coefficients
(1−4)x4
Subtract the numbers
−3x4
−3x4−1=0
Move the constant to the right-hand side and change its sign
−3x4=0+1
Removing 0 doesn't change the value,so remove it from the expression
−3x4=1
Change the signs on both sides of the equation
3x4=−1
Divide both sides
33x4=3−1
Divide the numbers
x4=3−1
Use b−a=−ba=−ba to rewrite the fraction
x4=−31
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4−31
Simplify the expression
More Steps

Evaluate
4−31
To take a root of a fraction,take the root of the numerator and denominator separately
4−341
Simplify the radical expression
4−31
Simplify the radical expression
More Steps

Evaluate
4−3
Rewrite the expression
43×(22+22i)
Apply the distributive property
43×22+43×22i
Multiply the numbers
2412+43×22i
Multiply the numbers
2412+2412i
2412+2412i1
Multiply by the Conjugate
(2412+2412i)(2412−2412i)2412−2412i
Calculate
More Steps

Evaluate
(2412+2412i)(2412−2412i)
Use (a+b)(a−b)=a2−b2 to simplify the product
(2412)2−(2412i)2
Evaluate the power
23−(2412i)2
Evaluate the power
23−(−23)
Calculate
3
32412−2412i
Simplify
23412−23412i
Rearrange the numbers
More Steps

Evaluate
23412
Multiply by the Conjugate
23×3412×3
Multiply the numbers
23×34108
Multiply the numbers
64108
64108−23412i
Rearrange the numbers
More Steps

Evaluate
−23412
Multiply by the Conjugate
23×3−412×3
Multiply the numbers
23×3−4108
Multiply the numbers
6−4108
Calculate
−64108
64108−64108i
x=±(64108−64108i)
Separate the equation into 2 possible cases
x=64108−64108ix=−64108+64108i
Solution
x1=−64108+64108i,x2=64108−64108i
Alternative Form
x1≈−0.537285+0.537285i,x2≈0.537285−0.537285i
Show Solution
