What times what= 2 but when added= -4 When the linear-quadratic equation is -1/2x^2-2x+7=-2x+5.
Is this two different questions?
1) What times what = 2 but when added = -4:
What times what = 2 ---> x · y = 2
When added = -4 ---> x + y = -4
Solving x · y = 2 for y: y = 2/x
Sustituting this into the other equation: x + y = -4 ---> x + 2/x = -4
multiplying both sides of this equation by x: x2 + 2 = -4x
adding 4x to both sides: x2 + 4x + 2 = 0
Using the quadratic formula when a = 1, b = 4, and c = 2: x = [ -4 +/- sqrt( 42 - 4·1·2 ) ] / ( 2·1)
x = [ -4 +/- sqrt(8) ] / 2
x = [ -4 +/- 2sqrt(2) ] / 2
One answer: x = -2 + sqrt(2)
Other answer: x = -2 - sqrt(2)
2) When the linear-quadratic equation is -1/2x2 - 2x + 7 = -2x + 5
-1/2x2 + 2 = 0
multiply both sides by -2: x2 - 4 = 0
(x + 2)(x - 2) = 0
One answer: x = -2
Other answer: x = 2
Is this two different questions?
1) What times what = 2 but when added = -4:
What times what = 2 ---> x · y = 2
When added = -4 ---> x + y = -4
Solving x · y = 2 for y: y = 2/x
Sustituting this into the other equation: x + y = -4 ---> x + 2/x = -4
multiplying both sides of this equation by x: x2 + 2 = -4x
adding 4x to both sides: x2 + 4x + 2 = 0
Using the quadratic formula when a = 1, b = 4, and c = 2: x = [ -4 +/- sqrt( 42 - 4·1·2 ) ] / ( 2·1)
x = [ -4 +/- sqrt(8) ] / 2
x = [ -4 +/- 2sqrt(2) ] / 2
One answer: x = -2 + sqrt(2)
Other answer: x = -2 - sqrt(2)
2) When the linear-quadratic equation is -1/2x2 - 2x + 7 = -2x + 5
-1/2x2 + 2 = 0
multiply both sides by -2: x2 - 4 = 0
(x + 2)(x - 2) = 0
One answer: x = -2
Other answer: x = 2