'-(x^2/2)-x-(5/2)' simplify

Given the quadratic equation:

-(x^2/2)-x-(5/2)

It can be written as

• - ½ x^2 - x - 5

a = -½, b = -1 c = -5

SImplify the quadratic equation.

Explanation:

In simplifying we must look for the common terms inside the equation, hence since we are given a quadratic equation, we must factor the value in order for it to be simplified.

It can be factored using the quadratic formula;

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the equation.

x = −b ± √(b^2 − 4ac)/2a

x = −(-1) ± √((-1)^2 − 4(-½)(-5)/2(-½)

x = 1 ± √(1 − 5)/-1

x = 1 ± √(-4)/-1

Since the value inside the equation is negative we will have no real roots, only complex number/imaginary number represented by “i”

x = -1 ± 2i

Final answer:

x = -1 ± 2i