Question
Simplify the expression
5x3−840x5
Evaluate
x2×5x−14x2×12x3×5
Multiply
More Steps

Multiply the terms
x2×5x
Multiply the terms with the same base by adding their exponents
x2+1×5
Add the numbers
x3×5
Use the commutative property to reorder the terms
5x3
5x3−14x2×12x3×5
Solution
More Steps

Multiply the terms
14x2×12x3×5
Multiply the terms
More Steps

Evaluate
14×12×5
Multiply the terms
168×5
Multiply the numbers
840
840x2×x3
Multiply the terms with the same base by adding their exponents
840x2+3
Add the numbers
840x5
5x3−840x5
Show Solution

Factor the expression
5x3(1−168x2)
Evaluate
x2×5x−14x2×12x3×5
Multiply
More Steps

Multiply the terms
x2×5x
Multiply the terms with the same base by adding their exponents
x2+1×5
Add the numbers
x3×5
Use the commutative property to reorder the terms
5x3
5x3−14x2×12x3×5
Multiply
More Steps

Multiply the terms
14x2×12x3×5
Multiply the terms
More Steps

Evaluate
14×12×5
Multiply the terms
168×5
Multiply the numbers
840
840x2×x3
Multiply the terms with the same base by adding their exponents
840x2+3
Add the numbers
840x5
5x3−840x5
Rewrite the expression
5x3−5x3×168x2
Solution
5x3(1−168x2)
Show Solution

Find the roots
x1=−8442,x2=0,x3=8442
Alternative Form
x1≈−0.077152,x2=0,x3≈0.077152
Evaluate
x2×5x−14x2×12x3×5
To find the roots of the expression,set the expression equal to 0
x2×5x−14x2×12x3×5=0
Multiply
More Steps

Multiply the terms
x2×5x
Multiply the terms with the same base by adding their exponents
x2+1×5
Add the numbers
x3×5
Use the commutative property to reorder the terms
5x3
5x3−14x2×12x3×5=0
Multiply
More Steps

Multiply the terms
14x2×12x3×5
Multiply the terms
More Steps

Evaluate
14×12×5
Multiply the terms
168×5
Multiply the numbers
840
840x2×x3
Multiply the terms with the same base by adding their exponents
840x2+3
Add the numbers
840x5
5x3−840x5=0
Factor the expression
5x3(1−168x2)=0
Divide both sides
x3(1−168x2)=0
Separate the equation into 2 possible cases
x3=01−168x2=0
The only way a power can be 0 is when the base equals 0
x=01−168x2=0
Solve the equation
More Steps

Evaluate
1−168x2=0
Move the constant to the right-hand side and change its sign
−168x2=0−1
Removing 0 doesn't change the value,so remove it from the expression
−168x2=−1
Change the signs on both sides of the equation
168x2=1
Divide both sides
168168x2=1681
Divide the numbers
x2=1681
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±1681
Simplify the expression
More Steps

Evaluate
1681
To take a root of a fraction,take the root of the numerator and denominator separately
1681
Simplify the radical expression
1681
Simplify the radical expression
2421
Multiply by the Conjugate
242×4242
Multiply the numbers
8442
x=±8442
Separate the equation into 2 possible cases
x=8442x=−8442
x=0x=8442x=−8442
Solution
x1=−8442,x2=0,x3=8442
Alternative Form
x1≈−0.077152,x2=0,x3≈0.077152
Show Solution
