Question
Simplify the expression
−12x3−27
Evaluate
−x2×12x−27
Solution
More Steps

Evaluate
−x2×12x
Multiply the terms with the same base by adding their exponents
−x2+1×12
Add the numbers
−x3×12
Use the commutative property to reorder the terms
−12x3
−12x3−27
Show Solution

Factor the expression
−3(4x3+9)
Evaluate
−x2×12x−27
Multiply
More Steps

Evaluate
x2×12x
Multiply the terms with the same base by adding their exponents
x2+1×12
Add the numbers
x3×12
Use the commutative property to reorder the terms
12x3
−12x3−27
Solution
−3(4x3+9)
Show Solution

Find the roots
x=−2318
Alternative Form
x≈−1.310371
Evaluate
−x2×12x−27
To find the roots of the expression,set the expression equal to 0
−x2×12x−27=0
Multiply
More Steps

Multiply the terms
x2×12x
Multiply the terms with the same base by adding their exponents
x2+1×12
Add the numbers
x3×12
Use the commutative property to reorder the terms
12x3
−12x3−27=0
Move the constant to the right-hand side and change its sign
−12x3=0+27
Removing 0 doesn't change the value,so remove it from the expression
−12x3=27
Change the signs on both sides of the equation
12x3=−27
Divide both sides
1212x3=12−27
Divide the numbers
x3=12−27
Divide the numbers
More Steps

Evaluate
12−27
Cancel out the common factor 3
4−9
Use b−a=−ba=−ba to rewrite the fraction
−49
x3=−49
Take the 3-th root on both sides of the equation
3x3=3−49
Calculate
x=3−49
Solution
More Steps

Evaluate
3−49
An odd root of a negative radicand is always a negative
−349
To take a root of a fraction,take the root of the numerator and denominator separately
−3439
Multiply by the Conjugate
34×342−39×342
Simplify
34×342−39×232
Multiply the numbers
More Steps

Evaluate
−39×232
Multiply the terms
−318×2
Use the commutative property to reorder the terms
−2318
34×342−2318
Multiply the numbers
More Steps

Evaluate
34×342
The product of roots with the same index is equal to the root of the product
34×42
Calculate the product
343
Transform the expression
326
Reduce the index of the radical and exponent with 3
22
22−2318
Reduce the fraction
More Steps

Evaluate
22−2
Use the product rule aman=an−m to simplify the expression
22−1−1
Subtract the terms
21−1
Simplify
2−1
2−318
Calculate
−2318
x=−2318
Alternative Form
x≈−1.310371
Show Solution
