Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
n=10
Evaluate
n(n−1)(n−2)=720
Expand the expression
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Evaluate
n(n−1)(n−2)
Multiply the terms
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Evaluate
n(n−1)
Apply the distributive property
n×n−n×1
Multiply the terms
n2−n×1
Any expression multiplied by 1 remains the same
n2−n
(n2−n)(n−2)
Apply the distributive property
n2×n−n2×2−n×n−(−n×2)
Multiply the terms
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Evaluate
n2×n
Use the product rule an×am=an+m to simplify the expression
n2+1
Add the numbers
n3
n3−n2×2−n×n−(−n×2)
Use the commutative property to reorder the terms
n3−2n2−n×n−(−n×2)
Multiply the terms
n3−2n2−n2−(−n×2)
Use the commutative property to reorder the terms
n3−2n2−n2−(−2n)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
n3−2n2−n2+2n
Subtract the terms
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Evaluate
−2n2−n2
Collect like terms by calculating the sum or difference of their coefficients
(−2−1)n2
Subtract the numbers
−3n2
n3−3n2+2n
n3−3n2+2n=720
Move the expression to the left side
n3−3n2+2n−720=0
Factor the expression
(n−10)(n2+7n+72)=0
Separate the equation into 2 possible cases
n−10=0n2+7n+72=0
Solve the equation
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Evaluate
n−10=0
Move the constant to the right-hand side and change its sign
n=0+10
Removing 0 doesn't change the value,so remove it from the expression
n=10
n=10n2+7n+72=0
Solve the equation
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Evaluate
n2+7n+72=0
Substitute a=1,b=7 and c=72 into the quadratic formula n=2a−b±b2−4ac
n=2−7±72−4×72
Simplify the expression
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Evaluate
72−4×72
Multiply the numbers
72−288
Evaluate the power
49−288
Subtract the numbers
−239
n=2−7±−239
The expression is undefined in the set of real numbers
n∈/R
n=10n∈/R
Solution
n=10
Show Solution
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