Question 1024905
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what two numbers multiply to negative 14 and add to 1??
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Let x and y be these two numbers. Then

x + y = 1,   (1)
xy = -14.    (2)

From (1) x = 1-y. Substitute it into (2). You will get

y*(1-y) = 14,   or

{{{y^2 + y + 14}}} = {{{0}}}.

Solve this quadratic equation by using the quadratic formula (factoring doesn't work):

{{{y[1,2]}}} = {{{(-1 +- sqrt(1^2 - 4*14))/2}}} = {{{(-1 +- sqrt(-55))/2}}}.

The roots are  {{{y[1]}}} = {{{(-1 + i*sqrt(55))/2}}}  and  {{{y[2]}}} = {{{(-1 - i*sqrt(55))/2}}}.

Thus the solutions to the problem are these two numbers 

{{{(1 + i*sqrt(55))/2}}}, {{{(1 - i*sqrt(55))/2}}}.
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