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Answer:
The numbers are 11 and -4
Step-by-step explanation:
Given
Let the two numbers be [tex]x[/tex] and [tex]y[/tex]
such that:
[tex]x + y = 7[/tex]
[tex]x*y = -44[/tex]
Required
Find x and y
Make y the subject in: [tex]x + y = 7[/tex]
[tex]y = 7 - x[/tex]
Substitute [tex]y = 7 - x[/tex] in [tex]x*y = -44[/tex]
[tex]x(7-x) = -44[/tex]
Open bracket
[tex]-x^2 +7x = -44[/tex]
Rewrite as:
[tex]x^2 -7x -44=0[/tex]
Expand
[tex]x^2 +4x-11x -44=0[/tex]
Factorize
[tex]x(x +4)-11(x +4)=0[/tex]
Factor out x + 4
[tex](x -11)(x +4)=0[/tex]
Solve for x
[tex]x =11; x =-4[/tex]
Recall that:
[tex]y = 7 - x[/tex]
So:
[tex]y = 7-11 = -4[/tex]
or
[tex]y = 7--4 = 11[/tex]