Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
j−2−700j3−29j2+51j+14
Evaluate
j−2−20j2×35j×1−20j−5−9j−2
Multiply the terms
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Multiply the terms
−20j2×35j×1
Rewrite the expression
−20j2×35j
Multiply the terms
−700j2×j
Multiply the terms with the same base by adding their exponents
−700j2+1
Add the numbers
−700j3
j−2−700j3−20j−5−9j−2
Use b−a=−ba=−ba to rewrite the fraction
−j−2700j3−20j−5−9j−2
Subtract the terms
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Evaluate
−20j−9j
Collect like terms by calculating the sum or difference of their coefficients
(−20−9)j
Subtract the numbers
−29j
−j−2700j3−29j−5−2
Subtract the numbers
−j−2700j3−29j−7
Reduce fractions to a common denominator
−j−2700j3−j−229j(j−2)−j−27(j−2)
Write all numerators above the common denominator
j−2−700j3−29j(j−2)−7(j−2)
Multiply the terms
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Evaluate
29j(j−2)
Multiply the terms
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Evaluate
29(j−2)
Apply the distributive property
29j−29×2
Multiply the numbers
29j−58
(29j−58)j
Apply the distributive property
29j×j−58j
Multiply the terms
29j2−58j
j−2−700j3−(29j2−58j)−7(j−2)
Multiply the terms
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Evaluate
7(j−2)
Apply the distributive property
7j−7×2
Multiply the numbers
7j−14
j−2−700j3−(29j2−58j)−(7j−14)
Solution
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Evaluate
−700j3−(29j2−58j)−(7j−14)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−700j3−29j2+58j−(7j−14)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−700j3−29j2+58j−7j+14
Subtract the terms
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Evaluate
58j−7j
Collect like terms by calculating the sum or difference of their coefficients
(58−7)j
Subtract the numbers
51j
−700j3−29j2+51j+14
j−2−700j3−29j2+51j+14
Show Solution
Find the excluded values
j=2
Evaluate
j−2−20j2×35j×1−20j−5−9j−2
To find the excluded values,set the denominators equal to 0
j−2=0
Move the constant to the right-hand side and change its sign
j=0+2
Solution
j=2
Show Solution
Find the roots
j≈0.342228
Evaluate
j−2−20j2×35j×1−20j−5−9j−2
To find the roots of the expression,set the expression equal to 0
j−2−20j2×35j×1−20j−5−9j−2=0
Find the domain
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Evaluate
j−2=0
Move the constant to the right side
j=0+2
Removing 0 doesn't change the value,so remove it from the expression
j=2
j−2−20j2×35j×1−20j−5−9j−2=0,j=2
Calculate
j−2−20j2×35j×1−20j−5−9j−2=0
Multiply the terms
More Steps
Multiply the terms
−20j2×35j×1
Rewrite the expression
−20j2×35j
Multiply the terms
−700j2×j
Multiply the terms with the same base by adding their exponents
−700j2+1
Add the numbers
−700j3
j−2−700j3−20j−5−9j−2=0
Use b−a=−ba=−ba to rewrite the fraction
−j−2700j3−20j−5−9j−2=0
Subtract the terms
More Steps
Simplify
−j−2700j3−20j
Reduce fractions to a common denominator
−j−2700j3−j−220j(j−2)
Write all numerators above the common denominator
j−2−700j3−20j(j−2)
Multiply the terms
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Evaluate
20j(j−2)
Multiply the terms
(20j−40)j
Apply the distributive property
20j×j−40j
Multiply the terms
20j2−40j
j−2−700j3−(20j2−40j)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
j−2−700j3−20j2+40j
j−2−700j3−20j2+40j−5−9j−2=0
Subtract the terms
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Simplify
j−2−700j3−20j2+40j−5
Reduce fractions to a common denominator
j−2−700j3−20j2+40j−j−25(j−2)
Write all numerators above the common denominator
j−2−700j3−20j2+40j−5(j−2)
Multiply the terms
More Steps
Evaluate
5(j−2)
Apply the distributive property
5j−5×2
Multiply the numbers
5j−10
j−2−700j3−20j2+40j−(5j−10)
Calculate the sum or difference
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Evaluate
−700j3−20j2+40j−(5j−10)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−700j3−20j2+40j−5j+10
Subtract the terms
−700j3−20j2+35j+10
j−2−700j3−20j2+35j+10
j−2−700j3−20j2+35j+10−9j−2=0
Subtract the terms
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Simplify
j−2−700j3−20j2+35j+10−9j
Reduce fractions to a common denominator
j−2−700j3−20j2+35j+10−j−29j(j−2)
Write all numerators above the common denominator
j−2−700j3−20j2+35j+10−9j(j−2)
Multiply the terms
More Steps
Evaluate
9j(j−2)
Multiply the terms
(9j−18)j
Apply the distributive property
9j×j−18j
Multiply the terms
9j2−18j
j−2−700j3−20j2+35j+10−(9j2−18j)
Calculate the sum or difference
More Steps
Evaluate
−700j3−20j2+35j+10−(9j2−18j)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−700j3−20j2+35j+10−9j2+18j
Subtract the terms
−700j3−29j2+35j+10+18j
Add the terms
−700j3−29j2+53j+10
j−2−700j3−29j2+53j+10
j−2−700j3−29j2+53j+10−2=0
Subtract the terms
More Steps
Simplify
j−2−700j3−29j2+53j+10−2
Reduce fractions to a common denominator
j−2−700j3−29j2+53j+10−j−22(j−2)
Write all numerators above the common denominator
j−2−700j3−29j2+53j+10−2(j−2)
Multiply the terms
More Steps
Evaluate
2(j−2)
Apply the distributive property
2j−2×2
Multiply the numbers
2j−4
j−2−700j3−29j2+53j+10−(2j−4)
Calculate the sum or difference
More Steps
Evaluate
−700j3−29j2+53j+10−(2j−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−700j3−29j2+53j+10−2j+4
Subtract the terms
−700j3−29j2+51j+10+4
Add the numbers
−700j3−29j2+51j+14
j−2−700j3−29j2+51j+14
j−2−700j3−29j2+51j+14=0
Cross multiply
−700j3−29j2+51j+14=(j−2)×0
Simplify the equation
−700j3−29j2+51j+14=0
Calculate
j≈0.342228
Check if the solution is in the defined range
j≈0.342228,j=2
Solution
j≈0.342228
Show Solution