x^2+2.25x-5=0

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Solution for x^2+2.25x-5=0 equation: 


Simplifying
x2 + 2.25x + -5 = 0

Reorder the terms:
-5 + 2.25x + x2 = 0

Solving
-5 + 2.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2.25x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 2.25x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2.25x + x2 = 0 + 5
2.25x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
2.25x + x2 = 5

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 = 5 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 5 + 1.265625

Combine like terms: 5 + 1.265625 = 6.265625
1.265625 + 2.25x + x2 = 6.265625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 6.265625

Calculate the square root of the right side: 2.503123049

Break this problem into two subproblems by setting 
(x + 1.125) equal to 2.503123049 and -2.503123049.


Subproblem 1
x + 1.125 = 2.503123049

Simplifying
x + 1.125 = 2.503123049

Reorder the terms:
1.125 + x = 2.503123049

Solving
1.125 + x = 2.503123049

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 = 2.503123049 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 2.503123049 + -1.125
x = 2.503123049 + -1.125

Combine like terms: 2.503123049 + -1.125 = 1.378123049
x = 1.378123049

Simplifying
x = 1.378123049


Subproblem 2
x + 1.125 = -2.503123049

Simplifying
x + 1.125 = -2.503123049

Reorder the terms:
1.125 + x = -2.503123049

Solving
1.125 + x = -2.503123049

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 = -2.503123049 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -2.503123049 + -1.125
x = -2.503123049 + -1.125

Combine like terms: -2.503123049 + -1.125 = -3.628123049
x = -3.628123049

Simplifying
x = -3.628123049


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.378123049, -3.628123049}

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