Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 3x – 5 = 0

Answer 1

The answer is x = 1.19 and x = -4.19

Answer 2

Answer: The required solution is

`x=1.19,~-4.19.`

Step-by-step explanation: We are given to solve the following quadratic equation by the method of completing the square :

`x^2+3x-5=0.`

We have

`x^2+3x-5=0\\\\\Rightarrow x^2+3x=5\\\\\Rightarrow x^2+2* x* (3)/(2)+\left((3)/(2)\right)^2=5+\left((3)/(2)\right)^2\\\\\\\Rightarrow \left(x+(3)/(2)\right)^2=5+(9)/(4)\\\\\\\Rightarrow x+(3)/(2)=\pm(√(29))/(2)\\\\\\\Rightarrow x=-(3)/(2)\pm(√(29))/(2)\\\\\\\Rightarrow x=(-3\pm√(29))/(2)\\\\\Rightarrow x=(-3\pm5.38)/(2)\\\\\\\Rightarrow x=(2.38)/(2),~~(-8.38)/(2)\\\\\\\Rightarrow x=1.19,~-4.19`

Thus, the required solution is

`x=1.19,~-4.19.`