Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
6x−x2−5x4
Evaluate
6x−1×x2−5x4
Solution
6x−x2−5x4
Show Solution
Factor the expression
x(1−x)(5x2+5x+6)
Evaluate
6x−1×x2−5x4
Any expression multiplied by 1 remains the same
6x−x2−5x4
Evaluate
−x2+6x−5x4
Rewrite the expression
x(−x)+x×6−x×5x3
Factor out x from the expression
x(−x+6−5x3)
Solution
More Steps
Evaluate
−x+6−5x3
Calculate
5x2+5x+6−5x3−5x2−6x
Rewrite the expression
5x2+5x+6−x×5x2−x×5x−x×6
Factor out −x from the expression
5x2+5x+6−x(5x2+5x+6)
Factor out 5x2+5x+6 from the expression
(1−x)(5x2+5x+6)
x(1−x)(5x2+5x+6)
Show Solution
Find the roots
x1=−21−1095i,x2=−21+1095i,x3=0,x4=1
Alternative Form
x1≈−0.5−0.974679i,x2≈−0.5+0.974679i,x3=0,x4=1
Evaluate
6x−1×x2−5x4
To find the roots of the expression,set the expression equal to 0
6x−1×x2−5x4=0
Any expression multiplied by 1 remains the same
6x−x2−5x4=0
Factor the expression
x(1−x)(5x2+5x+6)=0
Separate the equation into 3 possible cases
x=01−x=05x2+5x+6=0
Solve the equation
More Steps
Evaluate
1−x=0
Move the constant to the right-hand side and change its sign
−x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−x=−1
Change the signs on both sides of the equation
x=1
x=0x=15x2+5x+6=0
Solve the equation
More Steps
Evaluate
5x2+5x+6=0
Substitute a=5,b=5 and c=6 into the quadratic formula x=2a−b±b2−4ac
x=2×5−5±52−4×5×6
Simplify the expression
x=10−5±52−4×5×6
Simplify the expression
More Steps
Evaluate
52−4×5×6
Multiply the terms
52−120
Evaluate the power
25−120
Subtract the numbers
−95
x=10−5±−95
Simplify the radical expression
More Steps
Evaluate
−95
Evaluate the power
95×−1
Evaluate the power
95×i
x=10−5±95×i
Separate the equation into 2 possible cases
x=10−5+95×ix=10−5−95×i
Simplify the expression
x=−21+1095ix=10−5−95×i
Simplify the expression
x=−21+1095ix=−21−1095i
x=0x=1x=−21+1095ix=−21−1095i
Solution
x1=−21−1095i,x2=−21+1095i,x3=0,x4=1
Alternative Form
x1≈−0.5−0.974679i,x2≈−0.5+0.974679i,x3=0,x4=1
Show Solution