Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary x^2+3x=25

Answer 1

The solutions are:
`x= 3.72, -6.72`

Explanation:

`x^2+ 3x = 25\\ \\ x^2+3x+((3)/(2))^2 = 25 +((3)/(2))^2\\ \\ (x+(3)/(2))^2 = 25+(9)/(4)\\ \\ (x+(3)/(2))^2 =27.25\\ \\ \sqrt{(x+(3)/(2))^2} =\pm √(27.25) \\ \\ x+1.5= \pm √(27.25) \\ \\ x= -1.5 \pm √(27.25)\\ \\ x=-1.5+ √(27.25)=3.72015... \approx 3.72\\ \\ or\\ \\ x=-1.5-√(27.25) =-6.72015...\approx -6.72`

So, the solutions are:
`x= 3.72, -6.72`