### Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

(2): "2.23606798" was replaced by "(223606798/100000000)".

## Step by step solution :

## Step 1 :

` 111803399 Simplify ————————— 50000000 `

#### Equation at the end of step 1 :

111803399 ((x^{2}) + (————————— • x)) + 1 = 0 50000000## Step 2 :

#### Rewriting the whole as an Equivalent Fraction :

2.1Adding a fraction to a whole

Rewrite the whole as a fraction using 50000000 as the denominator :

` x`^{2} x^{2} • 50000000 x^{2} = —— = ————————————— 1 50000000

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

#### Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

` x`^{2} • 50000000 + 111803399x 50000000x^{2} + 111803399x —————————————————————————— = ——————————————————————— 50000000 50000000

#### Equation at the end of step 2 :

` (50000000x`^{2} + 111803399x) ————————————————————————— + 1 = 0 50000000

## Step 3 :

#### Rewriting the whole as an Equivalent Fraction :

3.1Adding a whole to a fraction

Rewrite the whole as a fraction using 50000000 as the denominator :

` 1 1 • 50000000 1 = — = ———————————— 1 50000000 `

## Step 4 :

#### Pulling out like terms :

4.1 Pull out like factors:

50000000x^{2} + 111803399x=x•(50000000x + 111803399)

#### Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

` x • (50000000x+111803399) + 50000000 50000000x`^{2} + 111803399x + 50000000 ———————————————————————————————————— = —————————————————————————————————— 50000000 50000000

#### Trying to factor by splitting the middle term

4.3Factoring 50000000x^{2} + 111803399x + 50000000

The first term is, 50000000x^{2} its coefficient is 50000000.

The middle term is, +111803399x its coefficient is 111803399.

The last term, "the constant", is +50000000

Step-1 : Multiply the coefficient of the first term by the constant

Numbers too big. Method shall not be applied

#### Equation at the end of step 4 :

` 50000000x`^{2} + 111803399x + 50000000 —————————————————————————————————— = 0 50000000

## Step 5 :

#### When a fraction equals zero :

`5.1 When a fraction equals zero ...`

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

` 50000000x`^{2}+111803399x+50000000 —————————————————————————————— • 50000000 = 0 • 50000000 50000000

Now, on the left hand side, the 50000000 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape:

50000000x^{2}+111803399x+50000000=0

#### Parabola, Finding the Vertex:

5.2Find the Vertex ofy = 50000000x^{2}+111803399x+50000000Parabolas have a highest or a lowest point called the Vertex.Our parabola opens up and accordingly has a lowest point (AKA absolute minimum).We know this even before plotting "y" because the coefficient of the first term,50000000, is positive (greater than zero).Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.For any parabola,Ax^{2}+Bx+C,the x-coordinate of the vertex is given by -B/(2A). In our case the x coordinate is -1.1180Plugging into the parabola formula -1.1180 for x we can calculate the y-coordinate:

y = 50000000.0 * -1.12 * -1.12 + 111803399.0 * -1.12 + 50000000.0

or y = -12500000.140

#### Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = 50000000x^{2}+111803399x+50000000

Axis of Symmetry (dashed) {x}={-1.12}

Vertex at {x,y} = {-1.12,-12500000.14}

x-Intercepts (Roots) :

Root 1 at {x,y} = {-1.62, 0.00}

Root 2 at {x,y} = {-0.62, 0.00}

### Solve Quadratic Equation using the Quadratic Formula

5.3Solving50000000x^{2}+111803399x+50000000 = 0 by the Quadratic Formula.According to the Quadratic Formula,x, the solution forAx^{2}+Bx+C= 0 , where A, B and C are numbers, often called coefficients, is given by :

-B± √B^{2}-4AC

x = ————————

2A In our case:

A=50000000.00

B=111803399.00

C= 50000000.00 B^{2} = 12500000027953200.00

4AC = 10000000000000000.00

B^{2}-4AC = 2500000027953200.00

SQRT(B^{2}-4AC)= 50000000.28

x=(-111803399.00±50000000.28)/100000000.00

x= -0.61803

x= -1.61803

## Two solutions were found :

- x= -1.61803

- x= -0.61803