x^2+2x-9.5625=0

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Solution for x^2+2x-9.5625=0 equation: 


Simplifying
x2 + 2x + -9.5625 = 0

Reorder the terms:
-9.5625 + 2x + x2 = 0

Solving
-9.5625 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9.5625' to each side of the equation.
-9.5625 + 2x + 9.5625 + x2 = 0 + 9.5625

Reorder the terms:
-9.5625 + 9.5625 + 2x + x2 = 0 + 9.5625

Combine like terms: -9.5625 + 9.5625 = 0.0000
0.0000 + 2x + x2 = 0 + 9.5625
2x + x2 = 0 + 9.5625

Combine like terms: 0 + 9.5625 = 9.5625
2x + x2 = 9.5625

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 9.5625 + 1

Reorder the terms:
1 + 2x + x2 = 9.5625 + 1

Combine like terms: 9.5625 + 1 = 10.5625
1 + 2x + x2 = 10.5625

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(x + 1) equal to 3.25 and -3.25.


Subproblem 1
x + 1 = 3.25

Simplifying
x + 1 = 3.25

Reorder the terms:
1 + x = 3.25

Solving
1 + x = 3.25

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.25 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.25 + -1
x = 3.25 + -1

Combine like terms: 3.25 + -1 = 2.25
x = 2.25

Simplifying
x = 2.25


Subproblem 2
x + 1 = -3.25

Simplifying
x + 1 = -3.25

Reorder the terms:
1 + x = -3.25

Solving
1 + x = -3.25

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.25 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.25 + -1
x = -3.25 + -1

Combine like terms: -3.25 + -1 = -4.25
x = -4.25

Simplifying
x = -4.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.25, -4.25}

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