x^2-2.25x-12=0

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Solution for x^2-2.25x-12=0 equation: 


Simplifying
x2 + -2.25x + -12 = 0

Reorder the terms:
-12 + -2.25x + x2 = 0

Solving
-12 + -2.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -2.25x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -2.25x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -2.25x + x2 = 0 + 12
-2.25x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-2.25x + x2 = 12

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 12 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 12 + 1.265625

Combine like terms: 12 + 1.265625 = 13.265625
1.265625 + -2.25x + x2 = 13.265625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 13.265625

Calculate the square root of the right side: 3.642200571

Break this problem into two subproblems by setting 
(x + -1.125) equal to 3.642200571 and -3.642200571.


Subproblem 1
x + -1.125 = 3.642200571

Simplifying
x + -1.125 = 3.642200571

Reorder the terms:
-1.125 + x = 3.642200571

Solving
-1.125 + x = 3.642200571

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 3.642200571 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 3.642200571 + 1.125
x = 3.642200571 + 1.125

Combine like terms: 3.642200571 + 1.125 = 4.767200571
x = 4.767200571

Simplifying
x = 4.767200571


Subproblem 2
x + -1.125 = -3.642200571

Simplifying
x + -1.125 = -3.642200571

Reorder the terms:
-1.125 + x = -3.642200571

Solving
-1.125 + x = -3.642200571

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -3.642200571 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -3.642200571 + 1.125
x = -3.642200571 + 1.125

Combine like terms: -3.642200571 + 1.125 = -2.517200571
x = -2.517200571

Simplifying
x = -2.517200571


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.767200571, -2.517200571}

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