Question
Simplify the expression
−2x3−3
Evaluate
x3−x2×3x−3
Multiply
More Steps

Multiply the terms
−x2×3x
Multiply the terms with the same base by adding their exponents
−x2+1×3
Add the numbers
−x3×3
Use the commutative property to reorder the terms
−3x3
x3−3x3−3
Solution
More Steps

Evaluate
x3−3x3
Collect like terms by calculating the sum or difference of their coefficients
(1−3)x3
Subtract the numbers
−2x3
−2x3−3
Show Solution

Find the roots
x=−2312
Alternative Form
x≈−1.144714
Evaluate
x3−x2×3x−3
To find the roots of the expression,set the expression equal to 0
x3−x2×3x−3=0
Multiply
More Steps

Multiply the terms
x2×3x
Multiply the terms with the same base by adding their exponents
x2+1×3
Add the numbers
x3×3
Use the commutative property to reorder the terms
3x3
x3−3x3−3=0
Subtract the terms
More Steps

Simplify
x3−3x3
Collect like terms by calculating the sum or difference of their coefficients
(1−3)x3
Subtract the numbers
−2x3
−2x3−3=0
Move the constant to the right-hand side and change its sign
−2x3=0+3
Removing 0 doesn't change the value,so remove it from the expression
−2x3=3
Change the signs on both sides of the equation
2x3=−3
Divide both sides
22x3=2−3
Divide the numbers
x3=2−3
Use b−a=−ba=−ba to rewrite the fraction
x3=−23
Take the 3-th root on both sides of the equation
3x3=3−23
Calculate
x=3−23
Solution
More Steps

Evaluate
3−23
An odd root of a negative radicand is always a negative
−323
To take a root of a fraction,take the root of the numerator and denominator separately
−3233
Multiply by the Conjugate
32×322−33×322
Simplify
32×322−33×34
Multiply the numbers
More Steps

Evaluate
−33×34
The product of roots with the same index is equal to the root of the product
−33×4
Calculate the product
−312
32×322−312
Multiply the numbers
More Steps

Evaluate
32×322
The product of roots with the same index is equal to the root of the product
32×22
Calculate the product
323
Reduce the index of the radical and exponent with 3
2
2−312
Calculate
−2312
x=−2312
Alternative Form
x≈−1.144714
Show Solution
