Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,848 users

please solve

0 votes
show how to solve and graph :)

|x²-3x-15|=25
asked Dec 19, 2014 in PRECALCULUS by anonymous

1 Answer

0 votes

The absolute value  equation is |x2 - 3x - 15| = 25

By splitting the equation into its two cases:

x2 - 3x - 15 = 25 or - (x2 - 3x - 15) =  25

 

Case 1 : Solve x2 - 3x - 15 = 25

x2 - 3x - 15 - 25 = 0

x2 - 3x  - 40 = 0

x2 - 8x + 5x - 40 = 0

x(x - 8) + 5(x - 8) = 0

(x - 8)(x + 5) = 0

x- 8 = 0 and x + 5 = 0

x = 8 and x = - 5

Solutions are x = 8 , x = - 5.

Case 2 : Solve  - (x2 - 3x - 15) =  25

Divide each by negative 1.

x2 - 3x - 15 = - 25

x2 - 3x - 15 + 25 = 0

x2 - 3x + 10 = 0

Compare it to image

Solutions are image.

image

image

image

image

image

Thus there are no real solutions in this case.

Graph

Graph the absolute function y = |x2 - 3x - 15|.

Graph the linear function y = 25.

Observe the graph the solutions of the equation x = 8 and x = - 5 are the abscissas of the intersection points of y = |x2 - 3x - 15| and y = 25.

answered Dec 19, 2014 by david Expert
edited Dec 19, 2014 by bradely

Related questions

asked Jan 19, 2015 in PRECALCULUS by anonymous
asked Jan 19, 2015 in PRECALCULUS by anonymous
asked Dec 19, 2014 in PRECALCULUS by anonymous
asked Dec 19, 2014 in PRECALCULUS by anonymous
asked Dec 9, 2014 in PRECALCULUS by anonymous
asked Nov 21, 2014 in PRECALCULUS by anonymous
asked Nov 21, 2014 in PRECALCULUS by anonymous
asked Nov 21, 2014 in PRECALCULUS by anonymous
asked Nov 21, 2014 in PRECALCULUS by anonymous
asked Nov 21, 2014 in PRECALCULUS by anonymous
asked Nov 21, 2014 in PRECALCULUS by anonymous
asked Nov 15, 2014 in PRECALCULUS by anonymous
asked Nov 5, 2014 in PRECALCULUS by anonymous
asked Nov 5, 2014 in PRECALCULUS by anonymous
asked Oct 29, 2014 in PRECALCULUS by anonymous
asked Dec 19, 2014 in PRECALCULUS by anonymous
asked Oct 22, 2014 in CALCULUS by anonymous
asked Oct 22, 2014 in CALCULUS by anonymous
asked Oct 22, 2014 in CALCULUS by anonymous
asked Oct 22, 2014 in CALCULUS by anonymous
...