Question

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

1.19, –4.19 –8.75, 5.75 1.66, 2.69 1.05, –4.05

Answer 1

x^2 + 3x - 5 = 0
x^2 + 3x = 5
x^2 + 3x + 2.25 = 5 + 2.25
(x + 1.5)^2 = 7.25
x + 1.5 = (+-) sqrt 7.25
x = -1.5 (+-) 2.69

x = -1.5 + 2.69 = 1.19 <=== ur answer
x = -1.5 - 2.69 = -4.19 <=== ur answer

Answer 2

1.19, –4.19 are correct option .

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 +
`(2)/(2)` * 3x -5 = 0.

On adding and subtracting the square of
`(3)/(2)`

`x^(2) + 2 * (3x)/(2) +((3)/(2)) ^(2) - ((3)/(2) )^(2) - 5 = 0`.

We can see first three terms are square

`(x+ (3)/(2) )^(2)` -
`((3)/(2)) ^(2)` -5 = 0

`(x+ (3)/(2) )^(2)` -
`((9)/(4))` -5 =0

On solving

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

On adding both sides by
`((29)/(4))`

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

Taking square root

`(x+(3)/(2))` = ±
`\sqrt{(29)/(4) }`.

`(x+(3)/(2))` = ±
`{(5.38)/(2) }`.

`(x+(3)/(2))` = ± 2.69 (it has two sign , so we will solve for both)

For + 2.69

On subtracting
`((3)/(2))` both side.

`(x+(3)/(2))` = + 2.69

x = + 2.69 -
`((3)/(2))`

x =
`((5.38 -3)/(2))`.

x =
`((2.38)/(2))`.

x = 1.19

For - 2.69

On subtracting
`((3)/(2))` both side.

`(x+(3)/(2))` = - 2.69

x = - 2.69 -
`((3)/(2))`

x =
`((-5.38 -3)/(2))`.

x =
`((-8.38)/(2))`.

x = - 4.19.

Therefore, 1.19, –4.19 are correct option .