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A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S....
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Transcript of A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S....
![Page 1: A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis.](https://reader035.fdocuments.in/reader035/viewer/2022070611/5a4d1bc57f8b9ab0599d44f2/html5/thumbnails/1.jpg)
A.5 Methods for A.5 Methods for Solving EquationsSolving Equations
Failures are finger posts on the road to achievement.-C. S. Lewis
![Page 2: A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis.](https://reader035.fdocuments.in/reader035/viewer/2022070611/5a4d1bc57f8b9ab0599d44f2/html5/thumbnails/2.jpg)
DomainRecall: The domain is the set of all x values for which an expression exists.
3x 23x 3 4x 2 9x 12
Ex. Find the domain of the following expression.
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Solving Rational EquationsRecall how to solve the following equation…
x2
13
5x6
![Page 4: A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis.](https://reader035.fdocuments.in/reader035/viewer/2022070611/5a4d1bc57f8b9ab0599d44f2/html5/thumbnails/4.jpg)
Steps for Solving Rational EquationsStep 1: Factor all denominators completely.
Step 2: Determine the least common denominator.
Step 3: Multiply both sides by the LCM (distribute!).
Step 4: Solve the new polynomial equation using learned methods.
Step 5: Check for any extraneous solutions in the original equation.
![Page 5: A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis.](https://reader035.fdocuments.in/reader035/viewer/2022070611/5a4d1bc57f8b9ab0599d44f2/html5/thumbnails/5.jpg)
Solving Rational EquationsSolve the equation.
3x 2
1x 1
7
(x 1)(x 2)
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Solving Rational EquationsWhat if we have one a little more tricky?!
53x 1
2
3x 2 5x 2
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Solving Quadratic Equations: GCF
x 2 2xSolve the equation. Solve the equation.
x 3 6x 2
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Completing the Square (a = 1)
x 2 6x 4 0
x 2 6x 4
(x 3)2 5
x 2 6x 95
Step 1: Move c to the other side
Step 2: Add to both sides
b2
2
Step 3: Rewrite the left side as the perfect square
x b2
2
Step 4: both sides and solve!
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Completing the Square (a ≠ 1)Solve the equation.
4x 2 8x 10
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Equations in Quadratic Form
2x 4 9x 2 350The following equation resembles quadratic form. Let’s solve it!
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Equations in Quadratic Form
(3x 4)2 6(3x 4) 160How can we solve this equation without multiplying it out?
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Solving Absolute Value Equations
x 7
What does “absolute value” mean?
What is the meaning of this equation?
2x 3 7
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Steps for Solving Absolute Value Equations
Step 1: Isolate absolute value on one side of the equation.
Step 2: Rewrite the equation, removing the absolute value, and plus/minus of the other side of the equation.
Step 3: Solve each equation for x.
Step 4: Check for any extraneous solutions in the original equation.
x a
x a
x a x a
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Solving Absolute Value EquationsSolve the following equation for x.
3x 1 92x
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A.5 Methods for A.5 Methods for Solving EquationsSolving Equations
Failures are finger posts on the road to achievement.-C. S. Lewis
Homework:Homework: