Question
Simplify the expression
−134x4−27
Evaluate
x4−5x3×27x−27
Multiply
More Steps

Multiply the terms
−5x3×27x
Multiply the terms
−135x3×x
Multiply the terms with the same base by adding their exponents
−135x3+1
Add the numbers
−135x4
x4−135x4−27
Solution
More Steps

Evaluate
x4−135x4
Collect like terms by calculating the sum or difference of their coefficients
(1−135)x4
Subtract the numbers
−134x4
−134x4−27
Show Solution

Find the roots
x1=−134454×673−134454×673i,x2=134454×673+134454×673i
Alternative Form
x1≈−0.473751−0.473751i,x2≈0.473751+0.473751i
Evaluate
x4−5x3×27x−27
To find the roots of the expression,set the expression equal to 0
x4−5x3×27x−27=0
Multiply
More Steps

Multiply the terms
5x3×27x
Multiply the terms
135x3×x
Multiply the terms with the same base by adding their exponents
135x3+1
Add the numbers
135x4
x4−135x4−27=0
Subtract the terms
More Steps

Simplify
x4−135x4
Collect like terms by calculating the sum or difference of their coefficients
(1−135)x4
Subtract the numbers
−134x4
−134x4−27=0
Move the constant to the right-hand side and change its sign
−134x4=0+27
Removing 0 doesn't change the value,so remove it from the expression
−134x4=27
Change the signs on both sides of the equation
134x4=−27
Divide both sides
134134x4=134−27
Divide the numbers
x4=134−27
Use b−a=−ba=−ba to rewrite the fraction
x4=−13427
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4−13427
Simplify the expression
More Steps

Evaluate
4−13427
To take a root of a fraction,take the root of the numerator and denominator separately
41344−27
Simplify the radical expression
More Steps

Evaluate
4−27
Rewrite the expression
427×(22+22i)
Apply the distributive property
427×22+427×22i
Multiply the numbers
24108+427×22i
Multiply the numbers
24108+24108i
413424108+24108i
Simplify
2467454+2467454i
Rearrange the numbers
More Steps

Evaluate
2467454
Multiply by the Conjugate
2467×4673454×4673
The product of roots with the same index is equal to the root of the product
2467×4673454×673
Multiply the numbers
134454×673
134454×673+2467454i
Rearrange the numbers
More Steps

Evaluate
2467454
Multiply by the Conjugate
2467×4673454×4673
The product of roots with the same index is equal to the root of the product
2467×4673454×673
Multiply the numbers
134454×673
134454×673+134454×673i
x=±(134454×673+134454×673i)
Separate the equation into 2 possible cases
x=134454×673+134454×673ix=−134454×673−134454×673i
Solution
x1=−134454×673−134454×673i,x2=134454×673+134454×673i
Alternative Form
x1≈−0.473751−0.473751i,x2≈0.473751+0.473751i
Show Solution
