Answer:
[tex]x^{2}+x =42[/tex]
Step-by-step explanation:
Let
x------> the number
we know that
The algebraic expression that represent the situation is equal to
[tex]x^{2}+x =42[/tex] ----> quadratic equation
using a graphing tool-----> to resolve the quadratic equation
see the attached figure
The solutions are
[tex]x=-7, x=6[/tex]
Verify each solution
For [tex]x=-7[/tex]
substitute in the expression
[tex]x^{2}+x =42[/tex]
[tex](-7)^{2}+(-7) =42[/tex]
[tex]49-7=42[/tex]
[tex]42=42[/tex] -----> is true
For [tex]x=6[/tex]
substitute in the expression
[tex]x^{2}+x =42[/tex]
[tex](6)^{2}+(6) =42[/tex]
[tex]36+6=42[/tex]
[tex]42=42[/tex] -----> is true
