Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x=0
Evaluate
−x3−∣x×1∣=x
Any expression multiplied by 1 remains the same
−x3−∣x∣=x
Move the expression to the left side
−x3−∣x∣−x=0
Separate the equation into 4 possible cases
−x3−x−x=0,x3≥0,x≥0−x3−(−x)−x=0,x3≥0,x<0−(−x3)−x−x=0,x3<0,x≥0−(−x3)−(−x)−x=0,x3<0,x<0
Solve the equation
More Steps
Evaluate
−x3−x−x=0
Calculate
More Steps
Evaluate
−x−x
Collect like terms by calculating the sum or difference of their coefficients
(−1−1)x
Subtract the numbers
−2x
−x3−2x=0
Factor the expression
−x(x2+2)=0
Divide both sides
x(x2+2)=0
Separate the equation into 2 possible cases
x=0x2+2=0
Solve the equation
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Evaluate
x2+2=0
Move the constant to the right-hand side and change its sign
x2=0−2
Removing 0 doesn't change the value,so remove it from the expression
x2=−2
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x
x∈/R
x=0x∈/R
Find the union
x=0
x=0,x3≥0,x≥0−x3−(−x)−x=0,x3≥0,x<0−(−x3)−x−x=0,x3<0,x≥0−(−x3)−(−x)−x=0,x3<0,x<0
The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0
x=0,x≥0,x≥0−x3−(−x)−x=0,x3≥0,x<0−(−x3)−x−x=0,x3<0,x≥0−(−x3)−(−x)−x=0,x3<0,x<0
Solve the equation
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Evaluate
−x3−(−x)−x=0
Calculate
−x3+x−x=0
Calculate the sum or difference
More Steps
Evaluate
−x3+x−x
The sum of two opposites equals 0
−x3+0
Remove 0
−x3
−x3=0
Change the signs on both sides of the equation
x3=0
The only way a power can be 0 is when the base equals 0
x=0
x=0,x≥0,x≥0x=0,x3≥0,x<0−(−x3)−x−x=0,x3<0,x≥0−(−x3)−(−x)−x=0,x3<0,x<0
The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0
x=0,x≥0,x≥0x=0,x≥0,x<0−(−x3)−x−x=0,x3<0,x≥0−(−x3)−(−x)−x=0,x3<0,x<0
Solve the equation
More Steps
Evaluate
−(−x3)−x−x=0
Calculate
x3−x−x=0
Calculate
More Steps
Evaluate
−x−x
Collect like terms by calculating the sum or difference of their coefficients
(−1−1)x
Subtract the numbers
−2x
x3−2x=0
Factor the expression
x(x2−2)=0
Separate the equation into 2 possible cases
x=0x2−2=0
Solve the equation
More Steps
Evaluate
x2−2=0
Move the constant to the right-hand side and change its sign
x2=0+2
Removing 0 doesn't change the value,so remove it from the expression
x2=2
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±2
Separate the equation into 2 possible cases
x=2x=−2
x=0x=2x=−2
x=0,x≥0,x≥0x=0,x≥0,x<0x=0x=2x=−2,x3<0,x≥0−(−x3)−(−x)−x=0,x3<0,x<0
The only way a base raised to an odd power can be less than 0 is if the base is less than 0
x=0,x≥0,x≥0x=0,x≥0,x<0x=0x=2x=−2,x<0,x≥0−(−x3)−(−x)−x=0,x3<0,x<0
The only way a power can be 0 is when the base equals 0
More Steps
Evaluate
−(−x3)−(−x)−x=0
Calculate
x3+x−x=0
Calculate the sum or difference
More Steps
Evaluate
x3+x−x
The sum of two opposites equals 0
x3+0
Remove 0
x3
x3=0
The only way a power can be 0 is when the base equals 0
x=0
x=0,x≥0,x≥0x=0,x≥0,x<0x=0x=2x=−2,x<0,x≥0x=0,x3<0,x<0
The only way a base raised to an odd power can be less than 0 is if the base is less than 0
x=0,x≥0,x≥0x=0,x≥0,x<0x=0x=2x=−2,x<0,x≥0x=0,x<0,x<0
Find the intersection
x=0x=0,x≥0,x<0x=0x=2x=−2,x<0,x≥0x=0,x<0,x<0
Find the intersection
x=0x∈∅x=0x=2x=−2,x<0,x≥0x=0,x<0,x<0
Find the intersection
x=0x∈∅x∈∅x=0,x<0,x<0
Find the intersection
x=0x∈∅x∈∅x∈∅
Solution
x=0
Show Solution
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