Question

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

Answer 1

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

$x^2+3x-5=0\\\\\Rightarrow x^2+3x=5\\\\\Rightarrow x^2+2\times x\times \dfrac{3}{2}+\left(\dfrac{3}{2}\right)^2=5+\left(\dfrac{3}{2}\right)^2\\\\\\\Rightarrow \left(x+\dfrac{3}{2}\right)^2=5+\dfrac{9}{4}\\\\\\\Rightarrow x+\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}\\\\\\\Rightarrow x=-\dfrac{3}{2}\pm\dfrac{\sqrt{29}}{2}\\\\\\\Rightarrow x=\dfrac{-3\pm\sqrt{29}}{2}\\\\\Rightarrow x=\dfrac{-3\pm5.38}{2}\\\\\\\Rightarrow x=\dfrac{2.38}{2},~~\dfrac{-8.38}{2}\\\\\\\Rightarrow x=1.19,~-4.19$

Thus, the required solution is

$x=1.19,~-4.19.$

Answer 2

The answer is x = 1.19 and x = -4.19