=2.82x^2-12.69x-7.05

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Solution for =2.82x^2-12.69x-7.05 equation: 


Simplifying
0 = 2.82x2 + -12.69x + -7.05

Reorder the terms:
0 = -7.05 + -12.69x + 2.82x2

Solving
0 = -7.05 + -12.69x + 2.82x2

Solving for variable 'x'.

Combine like terms: 0 + 7.05 = 7.05
7.05 + 12.69x + -2.82x2 = -7.05 + -12.69x + 2.82x2 + 7.05 + 12.69x + -2.82x2

Reorder the terms:
7.05 + 12.69x + -2.82x2 = -7.05 + 7.05 + -12.69x + 12.69x + 2.82x2 + -2.82x2

Combine like terms: -7.05 + 7.05 = 0.00
7.05 + 12.69x + -2.82x2 = 0.00 + -12.69x + 12.69x + 2.82x2 + -2.82x2
7.05 + 12.69x + -2.82x2 = -12.69x + 12.69x + 2.82x2 + -2.82x2

Combine like terms: -12.69x + 12.69x = 0.00
7.05 + 12.69x + -2.82x2 = 0.00 + 2.82x2 + -2.82x2
7.05 + 12.69x + -2.82x2 = 2.82x2 + -2.82x2

Combine like terms: 2.82x2 + -2.82x2 = 0.00
7.05 + 12.69x + -2.82x2 = 0.00

Begin completing the square.  Divide all terms by
-2.82 the coefficient of the squared term: 

Divide each side by '-2.82'.
-2.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -4.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -4.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -4.5x + x2 = 0 + 2.5
-4.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-4.5x + x2 = 2.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 2.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 2.5 + 5.0625

Combine like terms: 2.5 + 5.0625 = 7.5625
5.0625 + -4.5x + x2 = 7.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.75 and -2.75.


Subproblem 1
x + -2.25 = 2.75

Simplifying
x + -2.25 = 2.75

Reorder the terms:
-2.25 + x = 2.75

Solving
-2.25 + x = 2.75

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.75 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.75 + 2.25
x = 2.75 + 2.25

Combine like terms: 2.75 + 2.25 = 5
x = 5

Simplifying
x = 5


Subproblem 2
x + -2.25 = -2.75

Simplifying
x + -2.25 = -2.75

Reorder the terms:
-2.25 + x = -2.75

Solving
-2.25 + x = -2.75

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.75 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.75 + 2.25
x = -2.75 + 2.25

Combine like terms: -2.75 + 2.25 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, -0.5}

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