Answer:
1.19, –4.19 are correct option .
Step-by-step explanation:
Given : x² +3x -5 = 0.
To find : Solve the equation by completing the square. Round to the nearest hundredth .
Solution : We have given that
x² +3x -5 = 0.
On multiplying and divide by 2 to the term 3x .
x² +
* 3x -5 = 0.
On adding and subtracting the square of
.
We can see first three terms are square
-
-5 = 0
-
-5 =0
On solving
-
=0
On adding both sides by ![(\frac{29}{4})](https://tex.z-dn.net/?f=%28%5Cfrac%7B29%7D%7B4%7D%29)
= ![(\frac{29}{4})](https://tex.z-dn.net/?f=%28%5Cfrac%7B29%7D%7B4%7D%29)
Taking square root
= ±
.
= ±
.
= ± 2.69 (it has two sign , so we will solve for both)
For + 2.69
On subtracting
both side.
= + 2.69
x = + 2.69 - ![(\frac{3}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B2%7D%29)
x =
.
x =
.
x = 1.19
For - 2.69
On subtracting
both side.
= - 2.69
x = - 2.69 - ![(\frac{3}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B2%7D%29)
x =
.
x =
.
x = - 4.19.
Therefore, 1.19, –4.19 are correct option .