Question
Simplify the expression
x3x2x−9x×x−6x
Evaluate
3x23−9x21−6x−21
Rewrite the expression
More Steps

Evaluate
−6x−21
Express with a positive exponent using a−n=an1
−6×x211
Rewrite the expression
x21−6
Use b−a=−ba=−ba to rewrite the fraction
−x216
3x23−9x21−x216
Simplify the expression
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Evaluate
3x23
Use anm=nam to transform the expression
3x3
Simplify the radical expression
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Evaluate
x3
Rewrite the exponent as a sum
x2+1
Use am+n=am×an to expand the expression
x2×x
The root of a product is equal to the product of the roots of each factor
x2×x
Reduce the index of the radical and exponent with 2
xx
3xx
3xx−9x21−x216
Use anm=nam to transform the expression
3xx−9x−x216
Use anm=nam to transform the expression
3xx−9x−x6
Simplify
More Steps

Evaluate
−x6
Multiply by the Conjugate
−x×x6x
Calculate
−x6x
3xx−9x−x6x
Reduce fractions to a common denominator
x3xx×x−x9x×x−x6x
Write all numerators above the common denominator
x3xx×x−9x×x−6x
Solution
x3x2x−9x×x−6x
Show Solution

Find the roots
x=23+17
Alternative Form
x≈3.561553
Evaluate
3x23−9x21−6x−21
To find the roots of the expression,set the expression equal to 0
3x23−9x21−6x−21=0
Find the domain
3x23−9x21−6x−21=0,x>0
Calculate
3x23−9x21−6x−21=0
Rewrite the expression
More Steps

Evaluate
−6x−21
Express with a positive exponent using a−n=an1
−6×x211
Rewrite the expression
x21−6
Use b−a=−ba=−ba to rewrite the fraction
−x216
3x23−9x21−x216=0
Multiply both sides of the equation by LCD
(3x23−9x21−x216)x21=0×x21
Simplify the equation
More Steps

Evaluate
(3x23−9x21−x216)x21
Apply the distributive property
3x23×x21−9x21×x21−x216×x21
Simplify
3x23×x21−9x21×x21−6
Multiply the terms
More Steps

Evaluate
3x23×x21
Use anm=nam to transform the expression
3x3×x21
Simplify the radical expression
3xx×x21
Calculate
3x23x
3x23x−9x21×x21−6
Multiply the terms
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Evaluate
−9x21×x21
Use anm=nam to transform the expression
−9x×x21
Use the commutative property to reorder the terms
−9x21x
3x23x−9x21x−6
Rewrite the expression
3x2−9x21x−6
Rewrite the expression
3x2−9x−6
3x2−9x−6=0×x21
Any expression multiplied by 0 equals 0
3x2−9x−6=0
Substitute a=3,b=−9 and c=−6 into the quadratic formula x=2a−b±b2−4ac
x=2×39±(−9)2−4×3(−6)
Simplify the expression
x=69±(−9)2−4×3(−6)
Simplify the expression
More Steps

Evaluate
(−9)2−4×3(−6)
Multiply
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Multiply the terms
4×3(−6)
Rewrite the expression
−4×3×6
Multiply the terms
−72
(−9)2−(−72)
Rewrite the expression
92−(−72)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
92+72
Evaluate the power
81+72
Add the numbers
153
x=69±153
Simplify the radical expression
More Steps

Evaluate
153
Write the expression as a product where the root of one of the factors can be evaluated
9×17
Write the number in exponential form with the base of 3
32×17
The root of a product is equal to the product of the roots of each factor
32×17
Reduce the index of the radical and exponent with 2
317
x=69±317
Separate the equation into 2 possible cases
x=69+317x=69−317
Simplify the expression
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Evaluate
x=69+317
Divide the terms
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Evaluate
69+317
Rewrite the expression
63(3+17)
Cancel out the common factor 3
23+17
x=23+17
x=23+17x=69−317
Simplify the expression
More Steps

Evaluate
x=69−317
Divide the terms
More Steps

Evaluate
69−317
Rewrite the expression
63(3−17)
Cancel out the common factor 3
23−17
x=23−17
x=23+17x=23−17
Check if the solution is in the defined range
x=23+17x=23−17,x>0
Solution
x=23+17
Alternative Form
x≈3.561553
Show Solution
