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

Answer:

negative 5 plus or minus the square root of 17 divided by two: $x=\frac{-5\pm\sqrt{17}}{2}$.

Step-by-step 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.

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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.

$x=\frac{-5\pm\sqrt{5^2-4(1)(2)}}{2(1)}$

$x=\frac{-5\pm\sqrt{25-8}}{2}$

$x=\frac{-5\pm\sqrt{17}}{2}$.