Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
a1=−8,a2=−2,a3=2,a4=8
Evaluate
a216−16−a236=1
Find the domain
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Evaluate
{a2=016−a2=0
The only way a power can not be 0 is when the base not equals 0
{a=016−a2=0
Calculate
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Evaluate
16−a2=0
Rewrite the expression
−a2=−16
Change the signs on both sides of the equation
a2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±16
Simplify the expression
a=±4
Separate the inequality into 2 possible cases
{a=4a=−4
Find the intersection
a∈(−∞,−4)∪(−4,4)∪(4,+∞)
{a=0a∈(−∞,−4)∪(−4,4)∪(4,+∞)
Find the intersection
a∈(−∞,−4)∪(−4,0)∪(0,4)∪(4,+∞)
a216−16−a236=1,a∈(−∞,−4)∪(−4,0)∪(0,4)∪(4,+∞)
Multiply both sides of the equation by LCD
(a216−16−a236)a2(16−a2)=1×a2(16−a2)
Simplify the equation
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Evaluate
(a216−16−a236)a2(16−a2)
Apply the distributive property
a216×a2(16−a2)−16−a236×a2(16−a2)
Simplify
16(16−a2)−36a2
Expand the expression
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Calculate
16(16−a2)
Apply the distributive property
16×16−16a2
Multiply the numbers
256−16a2
256−16a2−36a2
Subtract the terms
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Evaluate
−16a2−36a2
Collect like terms by calculating the sum or difference of their coefficients
(−16−36)a2
Subtract the numbers
−52a2
256−52a2
256−52a2=1×a2(16−a2)
Simplify the equation
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Evaluate
1×a2(16−a2)
Any expression multiplied by 1 remains the same
a2(16−a2)
Apply the distributive property
a2×16−a2×a2
Use the commutative property to reorder the terms
16a2−a2×a2
Multiply the terms
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Evaluate
a2×a2
Use the product rule an×am=an+m to simplify the expression
a2+2
Add the numbers
a4
16a2−a4
256−52a2=16a2−a4
Move the expression to the left side
256−52a2−(16a2−a4)=0
Subtract the terms
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Evaluate
256−52a2−(16a2−a4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
256−52a2−16a2+a4
Subtract the terms
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Evaluate
−52a2−16a2
Collect like terms by calculating the sum or difference of their coefficients
(−52−16)a2
Subtract the numbers
−68a2
256−68a2+a4
256−68a2+a4=0
Factor the expression
(8−a)(2−a)(2+a)(8+a)=0
Separate the equation into 4 possible cases
8−a=02−a=02+a=08+a=0
Solve the equation
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Evaluate
8−a=0
Move the constant to the right-hand side and change its sign
−a=0−8
Removing 0 doesn't change the value,so remove it from the expression
−a=−8
Change the signs on both sides of the equation
a=8
a=82−a=02+a=08+a=0
Solve the equation
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Evaluate
2−a=0
Move the constant to the right-hand side and change its sign
−a=0−2
Removing 0 doesn't change the value,so remove it from the expression
−a=−2
Change the signs on both sides of the equation
a=2
a=8a=22+a=08+a=0
Solve the equation
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Evaluate
2+a=0
Move the constant to the right-hand side and change its sign
a=0−2
Removing 0 doesn't change the value,so remove it from the expression
a=−2
a=8a=2a=−28+a=0
Solve the equation
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Evaluate
8+a=0
Move the constant to the right-hand side and change its sign
a=0−8
Removing 0 doesn't change the value,so remove it from the expression
a=−8
a=8a=2a=−2a=−8
Check if the solution is in the defined range
a=8a=2a=−2a=−8,a∈(−∞,−4)∪(−4,0)∪(0,4)∪(4,+∞)
Find the intersection of the solution and the defined range
a=8a=2a=−2a=−8
Solution
a1=−8,a2=−2,a3=2,a4=8
Show Solution
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