2.25x^2-8x-7=0

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Solution for 2.25x^2-8x-7=0 equation: 


Simplifying
2.25x2 + -8x + -7 = 0

Reorder the terms:
-7 + -8x + 2.25x2 = 0

Solving
-7 + -8x + 2.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.25'.
-3.111111111 + -3.555555556x + x2 = 0

Move the constant term to the right:

Add '3.111111111' to each side of the equation.
-3.111111111 + -3.555555556x + 3.111111111 + x2 = 0 + 3.111111111

Reorder the terms:
-3.111111111 + 3.111111111 + -3.555555556x + x2 = 0 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + -3.555555556x + x2 = 0 + 3.111111111
-3.555555556x + x2 = 0 + 3.111111111

Combine like terms: 0 + 3.111111111 = 3.111111111
-3.555555556x + x2 = 3.111111111

The x term is -3.555555556x.  Take half its coefficient (-1.777777778).
Square it (3.160493828) and add it to both sides.

Add '3.160493828' to each side of the equation.
-3.555555556x + 3.160493828 + x2 = 3.111111111 + 3.160493828

Reorder the terms:
3.160493828 + -3.555555556x + x2 = 3.111111111 + 3.160493828

Combine like terms: 3.111111111 + 3.160493828 = 6.271604939
3.160493828 + -3.555555556x + x2 = 6.271604939

Factor a perfect square on the left side:
(x + -1.777777778)(x + -1.777777778) = 6.271604939

Calculate the square root of the right side: 2.50431726

Break this problem into two subproblems by setting 
(x + -1.777777778) equal to 2.50431726 and -2.50431726.


Subproblem 1
x + -1.777777778 = 2.50431726

Simplifying
x + -1.777777778 = 2.50431726

Reorder the terms:
-1.777777778 + x = 2.50431726

Solving
-1.777777778 + x = 2.50431726

Solving for variable 'x'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + x = 2.50431726 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + x = 2.50431726 + 1.777777778
x = 2.50431726 + 1.777777778

Combine like terms: 2.50431726 + 1.777777778 = 4.282095038
x = 4.282095038

Simplifying
x = 4.282095038


Subproblem 2
x + -1.777777778 = -2.50431726

Simplifying
x + -1.777777778 = -2.50431726

Reorder the terms:
-1.777777778 + x = -2.50431726

Solving
-1.777777778 + x = -2.50431726

Solving for variable 'x'.

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

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.777777778 + x = -2.50431726 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + x = -2.50431726 + 1.777777778
x = -2.50431726 + 1.777777778

Combine like terms: -2.50431726 + 1.777777778 = -0.726539482
x = -0.726539482

Simplifying
x = -0.726539482


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.282095038, -0.726539482}

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