x^2+2.25x=26.25

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Solution for x^2+2.25x=26.25 equation: 


Simplifying
x2 + 2.25x = 26.25

Reorder the terms:
2.25x + x2 = 26.25

Solving
2.25x + x2 = 26.25

Solving for variable 'x'.

Reorder the terms:
-26.25 + 2.25x + x2 = 26.25 + -26.25

Combine like terms: 26.25 + -26.25 = 0.00
-26.25 + 2.25x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '26.25' to each side of the equation.
-26.25 + 2.25x + 26.25 + x2 = 0.00 + 26.25

Reorder the terms:
-26.25 + 26.25 + 2.25x + x2 = 0.00 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + 2.25x + x2 = 0.00 + 26.25
2.25x + x2 = 0.00 + 26.25

Combine like terms: 0.00 + 26.25 = 26.25
2.25x + x2 = 26.25

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 = 26.25 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 26.25 + 1.265625

Combine like terms: 26.25 + 1.265625 = 27.515625
1.265625 + 2.25x + x2 = 27.515625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 27.515625

Calculate the square root of the right side: 5.245533815

Break this problem into two subproblems by setting 
(x + 1.125) equal to 5.245533815 and -5.245533815.


Subproblem 1
x + 1.125 = 5.245533815

Simplifying
x + 1.125 = 5.245533815

Reorder the terms:
1.125 + x = 5.245533815

Solving
1.125 + x = 5.245533815

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 = 5.245533815 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 5.245533815 + -1.125
x = 5.245533815 + -1.125

Combine like terms: 5.245533815 + -1.125 = 4.120533815
x = 4.120533815

Simplifying
x = 4.120533815


Subproblem 2
x + 1.125 = -5.245533815

Simplifying
x + 1.125 = -5.245533815

Reorder the terms:
1.125 + x = -5.245533815

Solving
1.125 + x = -5.245533815

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 = -5.245533815 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -5.245533815 + -1.125
x = -5.245533815 + -1.125

Combine like terms: -5.245533815 + -1.125 = -6.370533815
x = -6.370533815

Simplifying
x = -6.370533815


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.120533815, -6.370533815}

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