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Combining Methods for Solving Quadratic EquationsCombining Methods for Solving Quadratic Equations
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Question 1 of 5
1. Question
Solve for `x``3^(2x)3^x72=0`Hint
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Reducible equations are nonquadratic equations that can be reduced into a quadratic equation for easier solving.First, rewrite the equation as a quadratic equation by assigning a new variablelet`u=3^x``u^2=3^(2x)``3^(2x)3^x72` `=` `0` `u^2u72` `=` `0` Substitute new variable Solve for `u` by using cross method.`(u9)(u+8)` `=` `0` `u9` `=` `0` `u9` `+9` `=` `0` `+9` `u` `=` `9` `u+8` `=` `0` `u+8` `8` `=` `0` `8` `u` `=` `8` Finally, substitute `u=3^x` to get the values of `x``u` `=` `9` `3^x` `=` `9` Substitute `u=3^x` `3^x` `=` `3^2` `x` `=` `2` Equal bases means equal exponents `u` `=` `8` `3^x` `=` `8` Substitute `u=3^x` This has no solution since there is no `x` value that can make `3^x` negative`x=2` 
Question 2 of 5
2. Question
Solve for `x``2^(2x)3.2^x40=0`Hint
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Reducible equations are nonquadratic equations that can be reduced into a quadratic equation for easier solving.First, rewrite the equation as a quadratic equation by assigning a new variablelet`u=2^x``2^(2x)3.2^x40` `=` `0` `u^23u40` `=` `0` Substitute new variable Solve for `u` by using cross method.`(u+5)(u8)` `=` `0` `u+5` `=` `0` `u+5` `5` `=` `0` `5` `u` `=` `5` `u8` `=` `0` `u8` `+8` `=` `0` `+8` `u` `=` `8` Finally, substitute `u=2^x` to get the values of `x``u` `=` `8` `2^x` `=` `8` Substitute `u=2^x` `2^x` `=` `2^3` `x` `=` `3` Equal bases means equal exponents `u` `=` `5` `2^x` `=` `5` Substitute `u=2^x` This has no solution since there is no `x` value that can make `2^x` negative`x=3` 
Question 3 of 5
3. Question
Solve for `x``x^47x^218=0`Hint
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Nice Job!
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Reducible equations are nonquadratic equations that can be reduced into a quadratic equation for easier solving.First, rewrite the equation as a quadratic equation by assigning a new variablelet`u=x^2``x^47x^218` `=` `0` `u^27u18` `=` `0` Substitute new variable Solve for `u` by using cross method.`(u9)(u+2)` `=` `0` `u9` `=` `0` `u9` `+9` `=` `0` `+9` `u` `=` `9` `u+2` `=` `0` `u+2` `2` `=` `0` `2` `u` `=` `2` Finally, substitute `u=x^2` to get the values of `x``u` `=` `9` `x^2` `=` `9` Substitute `u=x^2` `sqrt(x^2)` `=` `sqrt9` Get the square root of both sides `x` `=` `+3` `u` `=` `2` `x^2` `=` `2` Substitute `u=x^2` This has no solution since there is no `x` value that can make `x^2` negative`x=3, 3` 
Question 4 of 5
4. Question
Solve for `x``4x^4+3x^210=0`Hint
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Excellent!
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Reducible equations are nonquadratic equations that can be reduced into a quadratic equation for easier solving.First, rewrite the equation as a quadratic equation by assigning a new variablelet`u=x^2``4x^4+3x^210` `=` `0` `4u^2+3u10` `=` `0` Substitute new variable Solve for `u` by using cross method.`(4u5)(u+2)` `=` `0` `4u5` `=` `0` `4u5` `+5` `=` `0` `+5` `4u` `=` `5` `u` `=` `5/4` `u+2` `=` `0` `u+2` `2` `=` `0` `2` `u` `=` `2` Finally, substitute `u=x^2` to get the values of `x``u` `=` `5/4` `x^2` `=` `5/4` Substitute `u=x^2` `sqrt(x^2)` `=` `sqrt(5/4)` Get the square root of both sides `x` `=` `+(sqrt5)/2` `u` `=` `2` `x^2` `=` `2` Substitute `u=x^2` This has no solution since there is no `x` value that can make `x^2` negative`x=(sqrt5)/2, (sqrt5)/2` 
Question 5 of 5
5. Question
Solve for `x``4^x+3*2^x10=0`Hint
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Fantastic!
Incorrect
Reducible equations are nonquadratic equations that can be reduced into a quadratic equation for easier solving.First, rewrite the equation as a quadratic equation by assigning a new variablelet`u=2^x``u^2=2^(2x)``4^x+3*2^x10` `=` `0` `(2^2)^x+3*2^x10` `=` `0` `2^(2x)+3*2^x10` `=` `0` `u^2+3u10` `=` `0` Substitute new variable Solve for `u` by using cross method.`(u2)(u+5)` `=` `0` `u2` `=` `0` `u2` `+2` `=` `0` `+2` `u` `=` `2` `u+5` `=` `0` `u+5` `5` `=` `0` `5` `u` `=` `5` Finally, substitute `u=2^x` to get the values of `x``u` `=` `2` `2^x` `=` `2` Substitute `u=2^x` `2^x` `=` `2^1` `x` `=` `1` Equal bases means equal exponents `u` `=` `5` `2^x` `=` `5` Substitute `u=2^x` This has no solution since there is no `x` value that can make `3^x` negative`x=1`
Quizzes
 Solve Quadratics by Factoring
 The Quadratic Formula
 Completing the Square 1
 Completing the Square 2
 Intro to Quadratic Functions (Parabolas) 1
 Intro to Quadratic Functions (Parabolas) 2
 Intro to Quadratic Functions (Parabolas) 3
 Graph Quadratic Functions in Standard Form 1
 Graph Quadratic Functions in Standard Form 2
 Graph Quadratic Functions by Completing the Square
 Graph Quadratic Functions in Vertex Form
 Write a Quadratic Equation from the Graph
 Write a Quadratic Equation Given the Vertex and Another Point
 Quadratic Inequalities 1
 Quadratic Inequalities 2
 Quadratics Word Problems 1
 Quadratics Word Problems 2
 Quadratic Identities
 Graphing Quadratics Using the Discriminant
 Positive and Negative Definite
 Applications of the Discriminant 1
 Applications of the Discriminant 2
 Combining Methods for Solving Quadratic Equations