x^2+6.5x+10.5=0

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Solution for x^2+6.5x+10.5=0 equation: 


Simplifying
x2 + 6.5x + 10.5 = 0

Reorder the terms:
10.5 + 6.5x + x2 = 0

Solving
10.5 + 6.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + 6.5x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + 6.5x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + 6.5x + x2 = 0 + -10.5
6.5x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
6.5x + x2 = -10.5

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -10.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -10.5 + 10.5625

Combine like terms: -10.5 + 10.5625 = 0.0625
10.5625 + 6.5x + x2 = 0.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(x + 3.25) equal to 0.25 and -0.25.


Subproblem 1
x + 3.25 = 0.25

Simplifying
x + 3.25 = 0.25

Reorder the terms:
3.25 + x = 0.25

Solving
3.25 + x = 0.25

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 0.25 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 0.25 + -3.25
x = 0.25 + -3.25

Combine like terms: 0.25 + -3.25 = -3
x = -3

Simplifying
x = -3


Subproblem 2
x + 3.25 = -0.25

Simplifying
x + 3.25 = -0.25

Reorder the terms:
3.25 + x = -0.25

Solving
3.25 + x = -0.25

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -0.25 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -0.25 + -3.25
x = -0.25 + -3.25

Combine like terms: -0.25 + -3.25 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3, -3.5}

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