Question
Solve the quadratic equation
Solve by factoring
Solve using the quadratic formula
Solve by completing the square
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n1=10,n2=90
Evaluate
30(n−30)=n(n−70)
Swap the sides
n(n−70)=30(n−30)
Expand the expression
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Evaluate
n(n−70)
Apply the distributive property
n×n−n×70
Multiply the terms
n2−n×70
Use the commutative property to reorder the terms
n2−70n
n2−70n=30(n−30)
Expand the expression
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Evaluate
30(n−30)
Apply the distributive property
30n−30×30
Multiply the numbers
30n−900
n2−70n=30n−900
Move the expression to the left side
n2−100n+900=0
Factor the expression
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Evaluate
n2−100n+900
Rewrite the expression
n2+(−10−90)n+900
Calculate
n2−10n−90n+900
Rewrite the expression
n×n−n×10−90n+90×10
Factor out n from the expression
n(n−10)−90n+90×10
Factor out −90 from the expression
n(n−10)−90(n−10)
Factor out n−10 from the expression
(n−90)(n−10)
(n−90)(n−10)=0
When the product of factors equals 0,at least one factor is 0
n−90=0n−10=0
Solve the equation for n
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Evaluate
n−90=0
Move the constant to the right-hand side and change its sign
n=0+90
Removing 0 doesn't change the value,so remove it from the expression
n=90
n=90n−10=0
Solve the equation for n
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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=90n=10
Solution
n1=10,n2=90
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