Question
Simplify the expression
−80k3−9
Evaluate
10k3−15k2×6k−9
Multiply
More Steps

Multiply the terms
−15k2×6k
Multiply the terms
−90k2×k
Multiply the terms with the same base by adding their exponents
−90k2+1
Add the numbers
−90k3
10k3−90k3−9
Solution
More Steps

Evaluate
10k3−90k3
Collect like terms by calculating the sum or difference of their coefficients
(10−90)k3
Subtract the numbers
−80k3
−80k3−9
Show Solution

Find the roots
k=−203900
Alternative Form
k≈−0.482745
Evaluate
10k3−15k2×6k−9
To find the roots of the expression,set the expression equal to 0
10k3−15k2×6k−9=0
Multiply
More Steps

Multiply the terms
15k2×6k
Multiply the terms
90k2×k
Multiply the terms with the same base by adding their exponents
90k2+1
Add the numbers
90k3
10k3−90k3−9=0
Subtract the terms
More Steps

Simplify
10k3−90k3
Collect like terms by calculating the sum or difference of their coefficients
(10−90)k3
Subtract the numbers
−80k3
−80k3−9=0
Move the constant to the right-hand side and change its sign
−80k3=0+9
Removing 0 doesn't change the value,so remove it from the expression
−80k3=9
Change the signs on both sides of the equation
80k3=−9
Divide both sides
8080k3=80−9
Divide the numbers
k3=80−9
Use b−a=−ba=−ba to rewrite the fraction
k3=−809
Take the 3-th root on both sides of the equation
3k3=3−809
Calculate
k=3−809
Solution
More Steps

Evaluate
3−809
An odd root of a negative radicand is always a negative
−3809
To take a root of a fraction,take the root of the numerator and denominator separately
−38039
Simplify the radical expression
More Steps

Evaluate
380
Write the expression as a product where the root of one of the factors can be evaluated
38×10
Write the number in exponential form with the base of 2
323×10
The root of a product is equal to the product of the roots of each factor
323×310
Reduce the index of the radical and exponent with 3
2310
−231039
Multiply by the Conjugate
2310×3102−39×3102
Simplify
2310×3102−39×3100
Multiply the numbers
More Steps

Evaluate
−39×3100
The product of roots with the same index is equal to the root of the product
−39×100
Calculate the product
−3900
2310×3102−3900
Multiply the numbers
More Steps

Evaluate
2310×3102
Multiply the terms
2×10
Multiply the terms
20
20−3900
Calculate
−203900
k=−203900
Alternative Form
k≈−0.482745
Show Solution
