Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x2−5)(x2+4)
Evaluate
x4−x2−20
Rewrite the expression
x4+(4−5)x2−20
Calculate
x4+4x2−5x2−20
Rewrite the expression
x2×x2+x2×4−5x2−5×4
Factor out x2 from the expression
x2(x2+4)−5x2−5×4
Factor out −5 from the expression
x2(x2+4)−5(x2+4)
Solution
(x2−5)(x2+4)
Show Solution
Find the roots
x1=−2i,x2=2i,x3=−5,x4=5
Alternative Form
x1=−2i,x2=2i,x3≈−2.236068,x4≈2.236068
Evaluate
x4−x2−20
To find the roots of the expression,set the expression equal to 0
x4−x2−20=0
Factor the expression
(x2−5)(x2+4)=0
Separate the equation into 2 possible cases
x2−5=0x2+4=0
Solve the equation
More Steps
Evaluate
x2−5=0
Move the constant to the right-hand side and change its sign
x2=0+5
Removing 0 doesn't change the value,so remove it from the expression
x2=5
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±5
Separate the equation into 2 possible cases
x=5x=−5
x=5x=−5x2+4=0
Solve the equation
More Steps
Evaluate
x2+4=0
Move the constant to the right-hand side and change its sign
x2=0−4
Removing 0 doesn't change the value,so remove it from the expression
x2=−4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−4
Simplify the expression
More Steps
Evaluate
−4
Evaluate the power
4×−1
Evaluate the power
4×i
Evaluate the square root
2i
x=±2i
Separate the equation into 2 possible cases
x=2ix=−2i
x=5x=−5x=2ix=−2i
Solution
x1=−2i,x2=2i,x3=−5,x4=5
Alternative Form
x1=−2i,x2=2i,x3≈−2.236068,x4≈2.236068
Show Solution