x^2+7x+8.25=0

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Solution for x^2+7x+8.25=0 equation: 


Simplifying
x2 + 7x + 8.25 = 0

Reorder the terms:
8.25 + 7x + x2 = 0

Solving
8.25 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8.25' to each side of the equation.
8.25 + 7x + -8.25 + x2 = 0 + -8.25

Reorder the terms:
8.25 + -8.25 + 7x + x2 = 0 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + 7x + x2 = 0 + -8.25
7x + x2 = 0 + -8.25

Combine like terms: 0 + -8.25 = -8.25
7x + x2 = -8.25

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -8.25 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -8.25 + 12.25

Combine like terms: -8.25 + 12.25 = 4
12.25 + 7x + x2 = 4

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2 and -2.


Subproblem 1
x + 3.5 = 2

Simplifying
x + 3.5 = 2

Reorder the terms:
3.5 + x = 2

Solving
3.5 + x = 2

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 2 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2 + -3.5
x = 2 + -3.5

Combine like terms: 2 + -3.5 = -1.5
x = -1.5

Simplifying
x = -1.5


Subproblem 2
x + 3.5 = -2

Simplifying
x + 3.5 = -2

Reorder the terms:
3.5 + x = -2

Solving
3.5 + x = -2

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -2 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2 + -3.5
x = -2 + -3.5

Combine like terms: -2 + -3.5 = -5.5
x = -5.5

Simplifying
x = -5.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.5, -5.5}

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