Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
5n3−4n2−320n
Evaluate
5n3−4n2−20n×16
Solution
5n3−4n2−320n
Show Solution
Factor the expression
n(5n2−4n−320)
Evaluate
5n3−4n2−20n×16
Multiply the terms
5n3−4n2−320n
Rewrite the expression
n×5n2−n×4n−n×320
Solution
n(5n2−4n−320)
Show Solution
Find the roots
n1=52−2401,n2=0,n3=52+2401
Alternative Form
n1≈−7.609994,n2=0,n3≈8.409994
Evaluate
5n3−4n2−20n×16
To find the roots of the expression,set the expression equal to 0
5n3−4n2−20n×16=0
Multiply the terms
5n3−4n2−320n=0
Factor the expression
n(5n2−4n−320)=0
Separate the equation into 2 possible cases
n=05n2−4n−320=0
Solve the equation
More Steps
Evaluate
5n2−4n−320=0
Substitute a=5,b=−4 and c=−320 into the quadratic formula n=2a−b±b2−4ac
n=2×54±(−4)2−4×5(−320)
Simplify the expression
n=104±(−4)2−4×5(−320)
Simplify the expression
More Steps
Evaluate
(−4)2−4×5(−320)
Multiply
(−4)2−(−6400)
Rewrite the expression
42−(−6400)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+6400
Evaluate the power
16+6400
Add the numbers
6416
n=104±6416
Simplify the radical expression
More Steps
Evaluate
6416
Write the expression as a product where the root of one of the factors can be evaluated
16×401
Write the number in exponential form with the base of 4
42×401
The root of a product is equal to the product of the roots of each factor
42×401
Reduce the index of the radical and exponent with 2
4401
n=104±4401
Separate the equation into 2 possible cases
n=104+4401n=104−4401
Simplify the expression
n=52+2401n=104−4401
Simplify the expression
n=52+2401n=52−2401
n=0n=52+2401n=52−2401
Solution
n1=52−2401,n2=0,n3=52+2401
Alternative Form
n1≈−7.609994,n2=0,n3≈8.409994
Show Solution