solve the equation by completing the square. round to the nearest hundredth if necessary. x^2+3x-5=0

Mathematics · High School · Tue Nov 03 2020

llm

Answered on Fri Apr 01 2022

Here, we have

x^2+3x-5=0

we have to solve the given equation by completing the square

Formula Used :

(a+b)^2 = a^2 + 2ab + b^2

(x)^2 + 2(x)(3/2) +(3/2)^2 -29/4 = 0 {9/4 - 29/4 = -5}

(x+3/2)^2 - 29/4 = 0

(x+3/2)^2 = 29/4

Taking square root on both sides, we get

x + 3/2 = ±√29/2

x = ±√29/2 - 3/2

Taking positive sign, we get

x= √29/2 - 3/2

x = 1.19

Now, taking negative sign, we get

x= -√29/2-3/2

x = -4.19

Thus, the required solution is 1.19 and -4.19