Respuesta :
The absolute value equation is [tex]x^{2} +x-8.75=0[/tex], if the solutions are x=2.5 and x=-3.5.
Step-by-step explanation:
The given is,
Two solutions: x = 2.5 and x = -3.5
Step:1
In this question we use reverse method of quadratic equation solve method,
From first solution, x = 2.5
x - 2.5 = 0..........................(1)
From the second solution, x = -3.5
x + 3.5 = 0.................(2)
From the equations (1) and (2),
( x - 2,5 ) ( x + 3.5 ) = 0
Multiply the equations,
[tex](x^{2} +3.5x-2.5x-8.75)=0[/tex]
[tex]x^{2} +x -8.75=0[/tex]
Step:2
Check for solution,
[tex]x^{2} +x -8.75=0[/tex]..........................(3)
Substitute the value of x=2.5 in above equation,
[tex]2.5^{2} +2.5 -8.75=0[/tex]
6.25 + 2.5 - 8.75 = 0
0 = 0
Result:
The absolute value equation is [tex]x^{2} +x-8.75=0[/tex], if the solutions are x=2.5 and x=-3.5.
