Question

Which of the following is a solution of x2 + 5x = −2?

5 plus or minus the square root of 33 divided by two.
5 plus or minus the square root of 17 divided by two
negative 5 plus or minus the square root of 33 divided by two.
negative 5 plus or minus the square root of 17 divided by two.

Answer 1

x^2 + 5x = -2
x^2 + 5x + 2 = 0

x = -b (+-) sqrt (b^2 - 4ac) / 2a
a = 1, b = 5, and c = 2

x = -5 (+-) sqrt (5^2 - 4(1)(2)) / 2(1)
x = -5 (+-) sqrt (25 - 8) / 2
x = -5 (+-) sqrt (17) / 2

answer is : negative 5 plus or minus the square root of 17 divided by 2

Answer 2

negative 5 plus or minus the square root of 17 divided by two:
`x=(-5\pm√(17))/(2)`.

Explanation:

We have the equation

`x^2+5x=-2`

`x^2+5x+2=0`.

To solve it, we are going to use the general formula. This formula is used to find the solutions of quadratic equations.

`x=(-b\pm√(b^2-4ac))/(2a)`

where a is the coefficient of
`x^2`, in this case a=1, b is the coefficient of x, in this case b=5 and c is the independent term, in this case c=2.

`x=(-5\pm√(5^2-4(1)(2)))/(2(1))`

`x=(-5\pm√(25-8))/(2)`

`x=(-5\pm√(17))/(2)`.