Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=0,x2=312
Alternative Form
x1=0,x2≈2.289428
Evaluate
x2×3x×8=2x6
Find the domain
More Steps
Evaluate
⎩⎨⎧x2≥03x×8≥02x6≥0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x
⎩⎨⎧x∈R3x×8≥02x6≥0
Calculate
More Steps
Evaluate
3x×8≥0
Multiply the terms
24x≥0
Rewrite the expression
x≥0
⎩⎨⎧x∈Rx≥02x6≥0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x
⎩⎨⎧x∈Rx≥0x∈R
Simplify
{x∈Rx≥0
Find the intersection
x≥0
x2×3x×8=2x6,x≥0
Simplify
More Steps
Evaluate
x2×3x×8
Calculate
x3x×8
Multiply the terms
x24x
x24x=2x6
Swap the sides
2x6=x24x
Evaluate
2x6=x24x,x24x≥0
Evaluate
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Evaluate
x24x≥0
Separate the inequality into 2 possible cases
{x≥024x≥0{x≤024x≤0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x
{x≥0x∈R{x≤024x≤0
Solve the inequality
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Evaluate
24x≤0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true only when 24x=0
24x=0
The only way a root could be 0 is when the radicand equals 0
24x=0
Rewrite the expression
x=0
{x≥0x∈R{x≤0x=0
Find the intersection
x≥0{x≤0x=0
Find the intersection
x≥0x=0
Find the union
x≥0
2x6=x24x,x≥0
Solve the equation for x
More Steps
Evaluate
2x6=x24x
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(2x6)2=(x24x)2
Evaluate the power
2x6=24x3
Add or subtract both sides
2x6−24x3=0
Factor the expression
2x3(x3−12)=0
Divide both sides
x3(x3−12)=0
Separate the equation into 2 possible cases
x3=0x3−12=0
The only way a power can be 0 is when the base equals 0
x=0x3−12=0
Solve the equation
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Evaluate
x3−12=0
Move the constant to the right-hand side and change its sign
x3=0+12
Removing 0 doesn't change the value,so remove it from the expression
x3=12
Take the 3-th root on both sides of the equation
3x3=312
Calculate
x=312
x=0x=312
x=0x=312,x≥0
Find the intersection of the solution and the defined range
x=0x=312
Check the solution
More Steps
Check the solution
02×3×0×8=2×06
Simplify
0=0
Evaluate
true
x=0x=312
Check the solution
More Steps
Check the solution
(312)2×3312×8=2(312)6
Simplify
16.970563=16.970563
Evaluate
true
x=0x=312
Solution
x1=0,x2=312
Alternative Form
x1=0,x2≈2.289428
Show Solution
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