Algebra
Calculus
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Question
Simplify the expression
−ξ2+6ξ
Evaluate
(9−(ξ−3)2)21
Subtract the terms
More Steps
Evaluate
9−(ξ−3)2
Expand the expression
9−ξ2+6ξ−9
Since two opposites add up to 0,remove them form the expression
−ξ2+6ξ
(−ξ2+6ξ)21
Solution
−ξ2+6ξ
Show Solution
Find the roots
ξ1=0,ξ2=6
Evaluate
(9−(ξ−3)2)21
To find the roots of the expression,set the expression equal to 0
(9−(ξ−3)2)21=0
Find the domain
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Evaluate
9−(ξ−3)2≥0
Add or subtract both sides
−(ξ−3)2≥0−9
Removing 0 doesn't change the value,so remove it from the expression
−(ξ−3)2≥−9
Change the signs on both sides of the inequality and flip the inequality sign
(ξ−3)2≤9
Take the 2-th root on both sides of the inequality
(ξ−3)2≤9
Calculate
∣ξ−3∣≤3
Separate the inequality into 2 possible cases
{ξ−3≤3ξ−3≥−3
Calculate
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Evaluate
ξ−3≤3
Move the constant to the right side
ξ≤3+3
Add the numbers
ξ≤6
{ξ≤6ξ−3≥−3
Cancel equal terms on both sides of the expression
{ξ≤6ξ≥0
Find the intersection
0≤ξ≤6
(9−(ξ−3)2)21=0,0≤ξ≤6
Calculate
(9−(ξ−3)2)21=0
Subtract the terms
More Steps
Simplify
9−(ξ−3)2
Expand the expression
9−ξ2+6ξ−9
Since two opposites add up to 0,remove them form the expression
−ξ2+6ξ
(−ξ2+6ξ)21=0
The only way a root could be 0 is when the radicand equals 0
−ξ2+6ξ=0
Factor the expression
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Evaluate
−ξ2+6ξ
Rewrite the expression
−ξ×ξ+ξ×6
Factor out −ξ from the expression
−ξ(ξ−6)
−ξ(ξ−6)=0
When the product of factors equals 0,at least one factor is 0
−ξ=0ξ−6=0
Solve the equation for ξ
ξ=0ξ−6=0
Solve the equation for ξ
More Steps
Evaluate
ξ−6=0
Move the constant to the right-hand side and change its sign
ξ=0+6
Removing 0 doesn't change the value,so remove it from the expression
ξ=6
ξ=0ξ=6
Check if the solution is in the defined range
ξ=0ξ=6,0≤ξ≤6
Find the intersection of the solution and the defined range
ξ=0ξ=6
Solution
ξ1=0,ξ2=6
Show Solution