Algebra
Calculus
Trigonometry
Matrix
Question
Solve the quadratic equation
Solve by factoring
Solve using the quadratic formula
Solve by completing the square
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a1=54,a2=81
Evaluate
4374=a(135−a)
Swap the sides
a(135−a)=4374
Expand the expression
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Evaluate
a(135−a)
Apply the distributive property
a×135−a×a
Use the commutative property to reorder the terms
135a−a×a
Multiply the terms
135a−a2
135a−a2=4374
Move the expression to the left side
135a−a2−4374=0
Factor the expression
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Evaluate
135a−a2−4374
Reorder the terms
−a2+135a−4374
Rewrite the expression
−a2+(54+81)a−4374
Calculate
−a2+54a+81a−4374
Rewrite the expression
−a×a+a×54+81a−81×54
Factor out −a from the expression
−a(a−54)+81a−81×54
Factor out 81 from the expression
−a(a−54)+81(a−54)
Factor out a−54 from the expression
(−a+81)(a−54)
(−a+81)(a−54)=0
When the product of factors equals 0,at least one factor is 0
−a+81=0a−54=0
Solve the equation for a
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Evaluate
−a+81=0
Move the constant to the right-hand side and change its sign
−a=0−81
Removing 0 doesn't change the value,so remove it from the expression
−a=−81
Change the signs on both sides of the equation
a=81
a=81a−54=0
Solve the equation for a
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Evaluate
a−54=0
Move the constant to the right-hand side and change its sign
a=0+54
Removing 0 doesn't change the value,so remove it from the expression
a=54
a=81a=54
Solution
a1=54,a2=81
Show Solution
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