Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−x2+6x
Evaluate
(9−(x−3)2)21
Subtract the terms
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Evaluate
9−(x−3)2
Expand the expression
9−x2+6x−9
Since two opposites add up to 0,remove them form the expression
−x2+6x
(−x2+6x)21
Solution
−x2+6x
Show Solution
Find the roots
x1=0,x2=6
Evaluate
(9−(x−3)2)21
To find the roots of the expression,set the expression equal to 0
(9−(x−3)2)21=0
Find the domain
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Evaluate
9−(x−3)2≥0
Add or subtract both sides
−(x−3)2≥0−9
Removing 0 doesn't change the value,so remove it from the expression
−(x−3)2≥−9
Change the signs on both sides of the inequality and flip the inequality sign
(x−3)2≤9
Take the 2-th root on both sides of the inequality
(x−3)2≤9
Calculate
∣x−3∣≤3
Separate the inequality into 2 possible cases
{x−3≤3x−3≥−3
Calculate
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Evaluate
x−3≤3
Move the constant to the right side
x≤3+3
Add the numbers
x≤6
{x≤6x−3≥−3
Cancel equal terms on both sides of the expression
{x≤6x≥0
Find the intersection
0≤x≤6
(9−(x−3)2)21=0,0≤x≤6
Calculate
(9−(x−3)2)21=0
Subtract the terms
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Simplify
9−(x−3)2
Expand the expression
9−x2+6x−9
Since two opposites add up to 0,remove them form the expression
−x2+6x
(−x2+6x)21=0
The only way a root could be 0 is when the radicand equals 0
−x2+6x=0
Factor the expression
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Evaluate
−x2+6x
Rewrite the expression
−x×x+x×6
Factor out −x from the expression
−x(x−6)
−x(x−6)=0
When the product of factors equals 0,at least one factor is 0
−x=0x−6=0
Solve the equation for x
x=0x−6=0
Solve the equation for x
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Evaluate
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x=0x=6
Check if the solution is in the defined range
x=0x=6,0≤x≤6
Find the intersection of the solution and the defined range
x=0x=6
Solution
x1=0,x2=6
Show Solution