please solve

Question

show how to solve and graph :)

|x²-3x-15|=25

Answer 1

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

Solutions are .

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.