Linear Algebra Examples

Find the Domain 9x^2-6x+1=0
Step 1
Factor using the perfect square rule.
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Step 1.1
Rewrite as .
Step 1.2
Rewrite as .
Step 1.3
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 1.4
Rewrite the polynomial.
Step 1.5
Factor using the perfect square trinomial rule , where and .
Step 2
Set the equal to .
Step 3
Solve for .
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Step 3.1
Add to both sides of the equation.
Step 3.2
Divide each term in by and simplify.
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Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
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Step 3.2.2.1
Cancel the common factor of .
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Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 4
The domain is the set of all valid values.
Step 5