Unit_9_MML_Worked_Problems - MM212CollegeAlgebra...

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MM212-College Algebra 1:00 PM ET – 2:00 PM ET Unit 9: More on Polynomials, Exponential and Logarithmic Functions 1) 9.1.11 Solve quadratic equations by the square root property. Concept and examples begin  on page 540. Solve the equation by using the square root property. (x - 8) 2  = 18 Steps for solving a quadratic equation using the square root property:  1) Write the equation in the proper form for using the square root property by isolating the squared variable  2) Take the square root of both sides of the equation and use the  ±  sign on the non-squared side. 3) Factor out and evaluate any perfect squares. 4) Check by substituting both solutions into the original equation. Note: MML states to simplify your answer. Use a comma to separate answers as needed. Express complex  numbers in terms of i. Type an exact answer, using radicals as needed. (x - 8) 2  = 18   We have a binomial squared and it is isolated so we move to step 2 and take the  square root of both sides of the equation. We must include the  ±  sign on the non-squared side. [(x - 8) 2 ] =  ±   [18]   Remember the square root of a squared binomial equals that binomial. x - 8 =  ±   [18]   We  have a multiple of a perfect square under the radical on the right side so  we will factor it out and evaluate it. x - 8 =  ±   [9 • 2] x - 8 =  ±   [9] •  [2] x - 8 =  ±  3 •  [2]   Next we will apply the additive inverse property to isolate the variable.  Convention is that we add the term before the plus minus sign rather than after the radical. x - 8 + 8 = 8  ±  3  [2] x = 8  ±  3  [2]   This is our final answer. 
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We will enter it into MML as:  8 + 3  [2],  8 - 3  [2]   since in MML you can use the radical  symbol and the line will go over the radicand, it isn't necessary to enclose the radicand by [ ]  as I have done above. 2) 9.1.21 Solve quadratic equations by the square root property. Concept and examples begin  on page 540. Solve the equation by using the square root property. 11x 2  - 9 = 0 Steps for solving a quadratic equation using the square root property:  1) Write the equation in the proper form for using the square root property by isolating the squared variable  2) Take the square root of both sides of the equation and use the  ±  sign on the non-squared side.
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