Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
4x3−12x2−75x
Evaluate
4x3−12x2−5x×15
Solution
4x3−12x2−75x
Show Solution
Factor the expression
x(4x2−12x−75)
Evaluate
4x3−12x2−5x×15
Multiply the terms
4x3−12x2−75x
Rewrite the expression
x×4x2−x×12x−x×75
Solution
x(4x2−12x−75)
Show Solution
Find the roots
x1=23−221,x2=0,x3=23+221
Alternative Form
x1≈−3.082576,x2=0,x3≈6.082576
Evaluate
4x3−12x2−5x×15
To find the roots of the expression,set the expression equal to 0
4x3−12x2−5x×15=0
Multiply the terms
4x3−12x2−75x=0
Factor the expression
x(4x2−12x−75)=0
Separate the equation into 2 possible cases
x=04x2−12x−75=0
Solve the equation
More Steps
Evaluate
4x2−12x−75=0
Substitute a=4,b=−12 and c=−75 into the quadratic formula x=2a−b±b2−4ac
x=2×412±(−12)2−4×4(−75)
Simplify the expression
x=812±(−12)2−4×4(−75)
Simplify the expression
More Steps
Evaluate
(−12)2−4×4(−75)
Multiply
(−12)2−(−1200)
Rewrite the expression
122−(−1200)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
122+1200
Evaluate the power
144+1200
Add the numbers
1344
x=812±1344
Simplify the radical expression
More Steps
Evaluate
1344
Write the expression as a product where the root of one of the factors can be evaluated
64×21
Write the number in exponential form with the base of 8
82×21
The root of a product is equal to the product of the roots of each factor
82×21
Reduce the index of the radical and exponent with 2
821
x=812±821
Separate the equation into 2 possible cases
x=812+821x=812−821
Simplify the expression
x=23+221x=812−821
Simplify the expression
x=23+221x=23−221
x=0x=23+221x=23−221
Solution
x1=23−221,x2=0,x3=23+221
Alternative Form
x1≈−3.082576,x2=0,x3≈6.082576
Show Solution