Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x3−4x2−54x
Evaluate
x3−4x2−3x×18
Solution
x3−4x2−54x
Show Solution
Factor the expression
x(x2−4x−54)
Evaluate
x3−4x2−3x×18
Multiply the terms
x3−4x2−54x
Rewrite the expression
x×x2−x×4x−x×54
Solution
x(x2−4x−54)
Show Solution
Find the roots
x1=2−58,x2=0,x3=2+58
Alternative Form
x1≈−5.615773,x2=0,x3≈9.615773
Evaluate
x3−4x2−3x×18
To find the roots of the expression,set the expression equal to 0
x3−4x2−3x×18=0
Multiply the terms
x3−4x2−54x=0
Factor the expression
x(x2−4x−54)=0
Separate the equation into 2 possible cases
x=0x2−4x−54=0
Solve the equation
More Steps
Evaluate
x2−4x−54=0
Substitute a=1,b=−4 and c=−54 into the quadratic formula x=2a−b±b2−4ac
x=24±(−4)2−4(−54)
Simplify the expression
More Steps
Evaluate
(−4)2−4(−54)
Multiply the numbers
(−4)2−(−216)
Rewrite the expression
42−(−216)
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+216
Evaluate the power
16+216
Add the numbers
232
x=24±232
Simplify the radical expression
More Steps
Evaluate
232
Write the expression as a product where the root of one of the factors can be evaluated
4×58
Write the number in exponential form with the base of 2
22×58
The root of a product is equal to the product of the roots of each factor
22×58
Reduce the index of the radical and exponent with 2
258
x=24±258
Separate the equation into 2 possible cases
x=24+258x=24−258
Simplify the expression
x=2+58x=24−258
Simplify the expression
x=2+58x=2−58
x=0x=2+58x=2−58
Solution
x1=2−58,x2=0,x3=2+58
Alternative Form
x1≈−5.615773,x2=0,x3≈9.615773
Show Solution