Question

Determine the solution to the system of equations given below y=x^2-5x+15

Answer 1

x=(5+i*sqrt(35))/2, (5-i*sqrt(35))/2

Explanation:

Use the quadratic formula with the following values.

a = 1

b = -5

c = 15

Substitute and simplify.

(5+-sqrt((-5)^2-4*(1*15)))/2*1

x = (5+-i*sqrt(35))/2

When you get a negative number inside the square root, remember that you can pull out i to make the number inside positive.

Answer 2

ANSWER


`x = (5)/(2) - ( √(35)i )/(2) \: or \: x = (5)/(2) + ( √(35)i )/(2)`

EXPLANATION

The given equation is


`y = {x}^(2) - 5x + 15`

To solve this equation, we equate it to zero.


`{x}^(2) - 5x + 15 = 0`

Comparing to ax²+bx+c=0, we have a=1, b=-5, c=15.

The solution is given by the quadratic formula,


`x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac } }{2a}`

We plug in the values to obtain,


`x = \frac{ - - 5\pm \sqrt{ {( - 5)}^(2) - 4(1)(15) } }{2(1)}`


`x = (5\pm √( 25 -60 ))/(2)`


`x = (5\pm √( - 35))/(2)`

Recall that,


`√(-1)=i`


`x = (5\pm √( 35)i)/(2)`


`x = (5)/(2) - ( √(35)i )/(2) \: or \: x = (5)/(2) + ( √(35)i )/(2)`