Question
Simplify the expression
x−6x2−162x
Evaluate
x−6x2−9x×18
Solution
x−6x2−162x
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Find the excluded values
x=6
Evaluate
x−6x2−9x×18
To find the excluded values,set the denominators equal to 0
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Solution
x=6
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Find the roots
x1=0,x2=162
Evaluate
x−6x2−9x×18
To find the roots of the expression,set the expression equal to 0
x−6x2−9x×18=0
Find the domain
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Evaluate
x−6=0
Move the constant to the right side
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x−6x2−9x×18=0,x=6
Calculate
x−6x2−9x×18=0
Multiply the terms
x−6x2−162x=0
Cross multiply
x2−162x=(x−6)×0
Simplify the equation
x2−162x=0
Factor the expression
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Evaluate
x2−162x
Rewrite the expression
x×x−x×162
Factor out x from the expression
x(x−162)
x(x−162)=0
When the product of factors equals 0,at least one factor is 0
x=0x−162=0
Solve the equation for x
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Evaluate
x−162=0
Move the constant to the right-hand side and change its sign
x=0+162
Removing 0 doesn't change the value,so remove it from the expression
x=162
x=0x=162
Check if the solution is in the defined range
x=0x=162,x=6
Find the intersection of the solution and the defined range
x=0x=162
Solution
x1=0,x2=162
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