Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=0,x2≈2.485584
Evaluate
2x3∣x−2∣=6x
Multiply the terms
2x3(x−2)=6x
Rewrite the expression
2x3(x−2)−6x=0
Separate the equation into 2 possible cases
2x3(x−2)−6x=0,2x3(x−2)≥0−2x3(x−2)−6x=0,2x3(x−2)<0
Solve the equation
More Steps
Evaluate
2x3(x−2)−6x=0
Calculate
More Steps
Evaluate
2x3(x−2)
Apply the distributive property
2x3×x−2x3×2
Multiply the terms
2x4−2x3×2
Multiply the numbers
2x4−4x3
2x4−4x3−6x=0
Factor the expression
2x(x3−2x2−3)=0
Divide both sides
x(x3−2x2−3)=0
Separate the equation into 2 possible cases
x=0x3−2x2−3=0
Solve the equation
x=0x≈2.485584
x=0x≈2.485584,2x3(x−2)≥0−2x3(x−2)−6x=0,2x3(x−2)<0
Solve the inequality
More Steps
Evaluate
2x3(x−2)≥0
Elimination the left coefficient
x3(x−2)≥0
Separate the inequality into 2 possible cases
{x3≥0x−2≥0{x3≤0x−2≤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≥0x−2≥0{x3≤0x−2≤0
Solve the inequality
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Evaluate
x−2≥0
Move the constant to the right side
x≥0+2
Removing 0 doesn't change the value,so remove it from the expression
x≥2
{x≥0x≥2{x3≤0x−2≤0
The only way a base raised to an odd power can be less than or equal to 0 is if the base is less than or equal to 0
{x≥0x≥2{x≤0x−2≤0
Solve the inequality
More Steps
Evaluate
x−2≤0
Move the constant to the right side
x≤0+2
Removing 0 doesn't change the value,so remove it from the expression
x≤2
{x≥0x≥2{x≤0x≤2
Find the intersection
x≥2{x≤0x≤2
Find the intersection
x≥2x≤0
Find the union
x∈(−∞,0]∪[2,+∞)
x=0x≈2.485584,x∈(−∞,0]∪[2,+∞)−2x3(x−2)−6x=0,2x3(x−2)<0
Solve the equation
More Steps
Evaluate
−2x3(x−2)−6x=0
Calculate
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Evaluate
−2x3(x−2)
Apply the distributive property
−2x3×x−(−2x3×2)
Multiply the terms
−2x4−(−2x3×2)
Multiply the numbers
−2x4−(−4x3)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−2x4+4x3
−2x4+4x3−6x=0
Factor the expression
−2x(x+1)(x2−3x+3)=0
Divide both sides
x(x+1)(x2−3x+3)=0
Separate the equation into 3 possible cases
x=0x+1=0x2−3x+3=0
Solve the equation
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Evaluate
x+1=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=−1x2−3x+3=0
Solve the equation
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Evaluate
x2−3x+3=0
Substitute a=1,b=−3 and c=3 into the quadratic formula x=2a−b±b2−4ac
x=23±(−3)2−4×3
Simplify the expression
x=23±−3
The expression is undefined in the set of real numbers
x∈/R
x=0x=−1x∈/R
Find the union
x=0x=−1
x=0x≈2.485584,x∈(−∞,0]∪[2,+∞)x=0x=−1,2x3(x−2)<0
Solve the inequality
More Steps
Evaluate
2x3(x−2)<0
Elimination the left coefficient
x3(x−2)<0
Separate the inequality into 2 possible cases
{x3>0x−2<0{x3<0x−2>0
The only way a base raised to an odd power can be greater than 0 is if the base is greater than 0
{x>0x−2<0{x3<0x−2>0
Solve the inequality
More Steps
Evaluate
x−2<0
Move the constant to the right side
x<0+2
Removing 0 doesn't change the value,so remove it from the expression
x<2
{x>0x<2{x3<0x−2>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>0x<2{x<0x−2>0
Solve the inequality
More Steps
Evaluate
x−2>0
Move the constant to the right side
x>0+2
Removing 0 doesn't change the value,so remove it from the expression
x>2
{x>0x<2{x<0x>2
Find the intersection
0<x<2{x<0x>2
Find the intersection
0<x<2x∈∅
Find the union
0<x<2
x=0x≈2.485584,x∈(−∞,0]∪[2,+∞)x=0x=−1,0<x<2
Find the intersection
x=0x≈2.485584x=0x=−1,0<x<2
Find the intersection
x=0x≈2.485584x∈∅
Find the union
x=0x≈2.485584
Solution
x1=0,x2≈2.485584
Show Solution
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