What two numbers multiply to -15 and can also add up to -7

1 answer:

8 0

Let the numbers be x and y
According to the data : xy=-15 and x+y=-7
xy=-15
x+y=-7

y=-7-x
x(-x-7)=-15

y=-7-x
-x^2-7x=-15

y=-7-x
x^2+7x-15=0

y=-7-x
x=(-7±sqrt(7*7+4*15))/2

y=-7-x
x=(-7±sqrt(109))/2

Goes to two systems.
1)
y=-7-x
x=(-7+sqrt(109))/2


y=-7+3.5-sqrt(109))/2
x=(-7+sqrt(109))/2

y=-3.5-sqrt(109))/2
x=(-7+sqrt(109))/2

2)
y=-7-x
x=(-7-sqrt(109))/2

y=-7+3.5+sqrt(109))/2
x=(-7-sqrt(109))/2

y=-3.5+sqrt(109))/2
x=(-7-sqrt(109))/2

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Find the value of x

soldier1979 [14.2K]

Answer:

x = -14

Step-by-step explanation:

Look at the image attatched. I have labeled the angles for better explanation.

We know that angle 1 is 54 degrees as is rests on a straight line with its adjacent angle at 126 degrees. This means that angle 1 would be 180 - 126 degrees, or 54 degrees. We also know that angle 1 and 3 must be congruent as the sides of the triangle opposite those angles are congruent as well. This means that both those angles are 54 degrees. Since the sum of all angles in a triangle must equal 180 degrees, we can get that angle 4 is 180 - (2*54) degrees, or 72. Since angle two and angle 4 both lie on a straight line, they must add up to 180 degrees. This means that the value of angle 2 would be 180 - 72, or 108 degrees. Since angle 2 is also equal to x+122, we get the equation:

108 = x + 122.

We then solve this by getting:

x = 108 - 122

which gives us the answer of

x = -14