Solve exactly no rounding 5x^2+1=-4x

Question

pleaseee help need answer 

Answer 1

Add 4x on both sides of equation.

 

5x² + 4x + 1 = 0

 

Now we have a quadratic equation.  We can use the quadratic formula to solve for x.

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 5

b = 4

c = 1

 

Plug in the values into the equation.

 

x = (-4 ± √(16 - 4(5))) / 10

x = (-4 ± √(-4)) / 10

 

Note that we cannot have a negative number under a square-root.  We can rewrite the √(-4) as

√(4) √(-1).

 

We know that √(-1) is equal to the imaginary number i.

 

x = (-4 ± 2i) / 10

 

 

Since we have a ± sign, we will have two solutions.

 

x = (-4 + 2i) / 10            and          x = (-4 - 2i) / 10

 

 

Answer 2

5x² + 1 = -4x

 

5x² + 4x + 1 = 0

 

Let's look at the discriminant from the quadratic formula:

 

b² - 4ac = 4² - 4(5)(1) = 16 - 20 = -4

 

Since the discriminant is less than zero, the solution will be a complex number.  Let's apply the full quadratic formula:

 

x = (-b/2a) ± (1/2a)√(b²-4ac)

 

x = -4/10 ± (1/10)√(-4)

 

x = -2/5 ± (1/5)i