Question

Which are the solutions of x^2 = –5x + 8?

Answer 1

x=​2​​−5+√​57​​​​​,​2​​−5−√​57​​​​​

I hope this helps. :)

Answer 2

Answer: The required solution is

`x=(-5\pm√(57))/(2).`

Step-by-step explanation: We are given to solve the following differential equation :

`x^2=-5x+8~~~~~~~~~~~~~~~~~~~~~~~(i)`

We will be using the method of completing the square to solve the given equation.

From equation (i), we have

`x^2=-5x+8\\\\\Rightarrow x^2+5x=8\\\\\Rightarrow x^2+2* x* (5)/(2)+\left((5)/(2)\right)^2=8+\left((5)/(2)\right)^2\\\\\\\Rightarrow \left(x+(5)/(2)\right)^2=8+(25)/(4)\\\\\\\Rightarrow \left(x+(5)/(2)\right)^2=(57)/(4)\\\\\\\Rightarrow x+(5)/(2)=\pm(√(57))/(2)\\\\\\\Rightarrow x=-(5)/(2)\pm(√(57))/(2)\\\\\\\Rightarrow x=(-5\pm√(57))/(2).`

Thus, the required solution is

`x=(-5\pm√(57))/(2).`