Question

Some of the steps for completing the square to solve

x2 + 5x = 2 are shown.


x2 + 5x = 2


x2 + 5x + (StartFraction 5 Over 2 EndFraction) squared = 2 + (StartFraction 5 Over 2 EndFraction) squared


(x + StartFraction 5 Over 2 EndFraction) squared = StartFraction 33 Over 4 EndFraction


Which are solutions of x2 + 5x = 2?

Answer 1

Answer: d and e

Explanation:

edge 2021 :)

Answer 2

Given:

The equation is:

`x^2+5x=2`

To find:

The solution of the given equation by completing the square.

Solution:

We have,

`x^2+5x=2`

We need to add the square of half of the coefficient of x on both sides.

Adding
`\left((5)/(2)\right)^2` on both sides, we get

`x^2+5x+\left((5)/(2)\right)^2=2+\left((5)/(2)\right)^2`

`\left(x+(5)/(2)\right)^2=2+(25)/(4)`

`\left(x+(5)/(2)\right)^2=(8+25)/(4)`

`\left(x+(5)/(2)\right)^2=(33)/(4)`

Taking square root on both sides, we get

`x+(5)/(2)=\pm \sqrt{(33)/(4)}`

`x=\pm (√(33))/(2)-(5)/(2)`

`x=(\pm √(33)-5)/(2)`

`x=(√(33)-5)/(2)` and
`x=(-√(33)-5)/(2)`

Therefore, the solutions of the given equation are
`x=(√(33)-5)/(2)` and
`x=(-√(33)-5)/(2)`.