Question
Simplify the expression
−40x3−42
Evaluate
−2x2×20x−42
Solution
More Steps

Evaluate
−2x2×20x
Multiply the terms
−40x2×x
Multiply the terms with the same base by adding their exponents
−40x2+1
Add the numbers
−40x3
−40x3−42
Show Solution

Factor the expression
−2(20x3+21)
Evaluate
−2x2×20x−42
Multiply
More Steps

Evaluate
−2x2×20x
Multiply the terms
−40x2×x
Multiply the terms with the same base by adding their exponents
−40x2+1
Add the numbers
−40x3
−40x3−42
Solution
−2(20x3+21)
Show Solution

Find the roots
x=−1031050
Alternative Form
x≈−1.016396
Evaluate
−2x2×20x−42
To find the roots of the expression,set the expression equal to 0
−2x2×20x−42=0
Multiply
More Steps

Multiply the terms
−2x2×20x
Multiply the terms
−40x2×x
Multiply the terms with the same base by adding their exponents
−40x2+1
Add the numbers
−40x3
−40x3−42=0
Move the constant to the right-hand side and change its sign
−40x3=0+42
Removing 0 doesn't change the value,so remove it from the expression
−40x3=42
Change the signs on both sides of the equation
40x3=−42
Divide both sides
4040x3=40−42
Divide the numbers
x3=40−42
Divide the numbers
More Steps

Evaluate
40−42
Cancel out the common factor 2
20−21
Use b−a=−ba=−ba to rewrite the fraction
−2021
x3=−2021
Take the 3-th root on both sides of the equation
3x3=3−2021
Calculate
x=3−2021
Solution
More Steps

Evaluate
3−2021
An odd root of a negative radicand is always a negative
−32021
To take a root of a fraction,take the root of the numerator and denominator separately
−320321
Multiply by the Conjugate
320×3202−321×3202
Simplify
320×3202−321×2350
Multiply the numbers
More Steps

Evaluate
−321×2350
Multiply the terms
−31050×2
Use the commutative property to reorder the terms
−231050
320×3202−231050
Multiply the numbers
More Steps

Evaluate
320×3202
The product of roots with the same index is equal to the root of the product
320×202
Calculate the product
3203
Reduce the index of the radical and exponent with 3
20
20−231050
Cancel out the common factor 2
10−31050
Calculate
−1031050
x=−1031050
Alternative Form
x≈−1.016396
Show Solution
