x^2+8x+9.75=0

Solution for x^2+8x+9.75=0 equation:

Simplifying
x2 + 8x + 9.75 = 0

Reorder the terms:
9.75 + 8x + x2 = 0

Solving
9.75 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9.75' to each side of the equation.
9.75 + 8x + -9.75 + x2 = 0 + -9.75

Reorder the terms:
9.75 + -9.75 + 8x + x2 = 0 + -9.75

Combine like terms: 9.75 + -9.75 = 0.00
0.00 + 8x + x2 = 0 + -9.75
8x + x2 = 0 + -9.75

Combine like terms: 0 + -9.75 = -9.75
8x + x2 = -9.75

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -9.75 + 16

Reorder the terms:
16 + 8x + x2 = -9.75 + 16

Combine like terms: -9.75 + 16 = 6.25
16 + 8x + x2 = 6.25

Factor a perfect square on the left side:
(x + 4)(x + 4) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(x + 4) equal to 2.5 and -2.5.

Subproblem 1
x + 4 = 2.5

Simplifying
x + 4 = 2.5

Reorder the terms:
4 + x = 2.5

Solving
4 + x = 2.5

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 2.5 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.5 + -4
x = 2.5 + -4

Combine like terms: 2.5 + -4 = -1.5
x = -1.5

Simplifying
x = -1.5

Subproblem 2
x + 4 = -2.5

Simplifying
x + 4 = -2.5

Reorder the terms:
4 + x = -2.5

Solving
4 + x = -2.5

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -2.5 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.5 + -4
x = -2.5 + -4

Combine like terms: -2.5 + -4 = -6.5
x = -6.5

Simplifying
x = -6.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.5, -6.5}