Question
Simplify the expression
a282a3−20−10a4
Evaluate
4a+85a−a220−3a−10a2−4a
Calculate the sum or difference
More Steps

Evaluate
4a+85a−3a−4a
Collect like terms by calculating the sum or difference of their coefficients
(4+85−3−4)a
Calculate the sum or difference
82a
82a−a220−10a2
Reduce fractions to a common denominator
a282a×a2−a220−a210a2×a2
Write all numerators above the common denominator
a282a×a2−20−10a2×a2
Multiply the terms
More Steps

Evaluate
a×a2
Use the product rule an×am=an+m to simplify the expression
a1+2
Add the numbers
a3
a282a3−20−10a2×a2
Solution
More Steps

Evaluate
a2×a2
Use the product rule an×am=an+m to simplify the expression
a2+2
Add the numbers
a4
a282a3−20−10a4
Show Solution

Find the excluded values
a=0
Evaluate
4a+85a−a220−3a−10a2−4a
To find the excluded values,set the denominators equal to 0
a2=0
Solution
a=0
Show Solution

Find the roots
a1≈0.642009,a2≈8.196368
Evaluate
4a+85a−a220−3a−10a2−4a
To find the roots of the expression,set the expression equal to 0
4a+85a−a220−3a−10a2−4a=0
The only way a power can not be 0 is when the base not equals 0
4a+85a−a220−3a−10a2−4a=0,a=0
Calculate
4a+85a−a220−3a−10a2−4a=0
Add the terms
More Steps

Evaluate
4a+85a
Collect like terms by calculating the sum or difference of their coefficients
(4+85)a
Add the numbers
89a
89a−a220−3a−10a2−4a=0
Subtract the terms
More Steps

Simplify
89a−a220
Reduce fractions to a common denominator
a289a×a2−a220
Write all numerators above the common denominator
a289a×a2−20
Multiply the terms
More Steps

Evaluate
a×a2
Use the product rule an×am=an+m to simplify the expression
a1+2
Add the numbers
a3
a289a3−20
a289a3−20−3a−10a2−4a=0
Subtract the terms
More Steps

Simplify
a289a3−20−3a
Reduce fractions to a common denominator
a289a3−20−a23a×a2
Write all numerators above the common denominator
a289a3−20−3a×a2
Multiply the terms
More Steps

Evaluate
a×a2
Use the product rule an×am=an+m to simplify the expression
a1+2
Add the numbers
a3
a289a3−20−3a3
Subtract the terms
More Steps

Evaluate
89a3−3a3
Collect like terms by calculating the sum or difference of their coefficients
(89−3)a3
Subtract the numbers
86a3
a286a3−20
a286a3−20−10a2−4a=0
Subtract the terms
More Steps

Simplify
a286a3−20−10a2
Reduce fractions to a common denominator
a286a3−20−a210a2×a2
Write all numerators above the common denominator
a286a3−20−10a2×a2
Multiply the terms
More Steps

Evaluate
a2×a2
Use the product rule an×am=an+m to simplify the expression
a2+2
Add the numbers
a4
a286a3−20−10a4
a286a3−20−10a4−4a=0
Subtract the terms
More Steps

Simplify
a286a3−20−10a4−4a
Reduce fractions to a common denominator
a286a3−20−10a4−a24a×a2
Write all numerators above the common denominator
a286a3−20−10a4−4a×a2
Multiply the terms
More Steps

Evaluate
a×a2
Use the product rule an×am=an+m to simplify the expression
a1+2
Add the numbers
a3
a286a3−20−10a4−4a3
Subtract the terms
More Steps

Evaluate
86a3−4a3
Collect like terms by calculating the sum or difference of their coefficients
(86−4)a3
Subtract the numbers
82a3
a282a3−20−10a4
a282a3−20−10a4=0
Cross multiply
82a3−20−10a4=a2×0
Simplify the equation
82a3−20−10a4=0
Factor the expression
2(41a3−10−5a4)=0
Divide both sides
41a3−10−5a4=0
Calculate
a≈0.642009a≈8.196368
Check if the solution is in the defined range
a≈0.642009a≈8.196368,a=0
Find the intersection of the solution and the defined range
a≈0.642009a≈8.196368
Solution
a1≈0.642009,a2≈8.196368
Show Solution
