Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
4t3−4t2−225t
Evaluate
4t3−4t2−15t×15
Solution
4t3−4t2−225t
Show Solution
Factor the expression
t(4t2−4t−225)
Evaluate
4t3−4t2−15t×15
Multiply the terms
4t3−4t2−225t
Rewrite the expression
t×4t2−t×4t−t×225
Solution
t(4t2−4t−225)
Show Solution
Find the roots
t1=21−226,t2=0,t3=21+226
Alternative Form
t1≈−7.016648,t2=0,t3≈8.016648
Evaluate
4t3−4t2−15t×15
To find the roots of the expression,set the expression equal to 0
4t3−4t2−15t×15=0
Multiply the terms
4t3−4t2−225t=0
Factor the expression
t(4t2−4t−225)=0
Separate the equation into 2 possible cases
t=04t2−4t−225=0
Solve the equation
More Steps
Evaluate
4t2−4t−225=0
Substitute a=4,b=−4 and c=−225 into the quadratic formula t=2a−b±b2−4ac
t=2×44±(−4)2−4×4(−225)
Simplify the expression
t=84±(−4)2−4×4(−225)
Simplify the expression
More Steps
Evaluate
(−4)2−4×4(−225)
Multiply
(−4)2−(−3600)
Rewrite the expression
42−(−3600)
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+3600
Evaluate the power
16+3600
Add the numbers
3616
t=84±3616
Simplify the radical expression
More Steps
Evaluate
3616
Write the expression as a product where the root of one of the factors can be evaluated
16×226
Write the number in exponential form with the base of 4
42×226
The root of a product is equal to the product of the roots of each factor
42×226
Reduce the index of the radical and exponent with 2
4226
t=84±4226
Separate the equation into 2 possible cases
t=84+4226t=84−4226
Simplify the expression
t=21+226t=84−4226
Simplify the expression
t=21+226t=21−226
t=0t=21+226t=21−226
Solution
t1=21−226,t2=0,t3=21+226
Alternative Form
t1≈−7.016648,t2=0,t3≈8.016648
Show Solution