Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
∣x∣−x2
Evaluate
∣x×1∣−x2
Any expression multiplied by 1 remains the same
∣x∣−x2
Solution
∣x∣−x2
Show Solution
Find the roots
x1=−1,x2=0,x3=1
Evaluate
∣x×1∣−x2
To find the roots of the expression,set the expression equal to 0
∣x×1∣−x2=0
Any expression multiplied by 1 remains the same
∣x∣−x2=0
When the expression in absolute value bars is not negative, remove the bars
∣x∣−x2=0
Separate the equation into 2 possible cases
x−x2=0,x≥0−x−x2=0,x<0
Solve the equation
More Steps
Evaluate
x−x2=0
Factor the expression
More Steps
Evaluate
x−x2
Rewrite the expression
x−x×x
Factor out x from the expression
x(1−x)
x(1−x)=0
When the product of factors equals 0,at least one factor is 0
x=01−x=0
Solve the equation for x
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=1
x=0x=1,x≥0−x−x2=0,x<0
Solve the equation
More Steps
Evaluate
−x−x2=0
Factor the expression
More Steps
Evaluate
−x−x2
Rewrite the expression
−x−x×x
Factor out −x from the expression
−x(1+x)
−x(1+x)=0
When the product of factors equals 0,at least one factor is 0
−x=01+x=0
Solve the equation for x
x=01+x=0
Solve the equation for x
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
x=0x=−1
x=0x=1,x≥0x=0x=−1,x<0
Find the intersection
x=0x=1x=0x=−1,x<0
Find the intersection
x=0x=1x=−1
Solution
x1=−1,x2=0,x3=1
Show Solution