x*x+21.75x=-15.75

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Solution for x*x+21.75x=-15.75 equation: 


Simplifying
x * x + 21.75x = -15.75

Multiply x * x
x2 + 21.75x = -15.75

Reorder the terms:
21.75x + x2 = -15.75

Solving
21.75x + x2 = -15.75

Solving for variable 'x'.

Reorder the terms:
15.75 + 21.75x + x2 = -15.75 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
15.75 + 21.75x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-15.75' to each side of the equation.
15.75 + 21.75x + -15.75 + x2 = 0.00 + -15.75

Reorder the terms:
15.75 + -15.75 + 21.75x + x2 = 0.00 + -15.75

Combine like terms: 15.75 + -15.75 = 0.00
0.00 + 21.75x + x2 = 0.00 + -15.75
21.75x + x2 = 0.00 + -15.75

Combine like terms: 0.00 + -15.75 = -15.75
21.75x + x2 = -15.75

The x term is 21.75x.  Take half its coefficient (10.875).
Square it (118.265625) and add it to both sides.

Add '118.265625' to each side of the equation.
21.75x + 118.265625 + x2 = -15.75 + 118.265625

Reorder the terms:
118.265625 + 21.75x + x2 = -15.75 + 118.265625

Combine like terms: -15.75 + 118.265625 = 102.515625
118.265625 + 21.75x + x2 = 102.515625

Factor a perfect square on the left side:
(x + 10.875)(x + 10.875) = 102.515625

Calculate the square root of the right side: 10.125

Break this problem into two subproblems by setting 
(x + 10.875) equal to 10.125 and -10.125.


Subproblem 1
x + 10.875 = 10.125

Simplifying
x + 10.875 = 10.125

Reorder the terms:
10.875 + x = 10.125

Solving
10.875 + x = 10.125

Solving for variable 'x'.

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

Add '-10.875' to each side of the equation.
10.875 + -10.875 + x = 10.125 + -10.875

Combine like terms: 10.875 + -10.875 = 0.000
0.000 + x = 10.125 + -10.875
x = 10.125 + -10.875

Combine like terms: 10.125 + -10.875 = -0.75
x = -0.75

Simplifying
x = -0.75


Subproblem 2
x + 10.875 = -10.125

Simplifying
x + 10.875 = -10.125

Reorder the terms:
10.875 + x = -10.125

Solving
10.875 + x = -10.125

Solving for variable 'x'.

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

Add '-10.875' to each side of the equation.
10.875 + -10.875 + x = -10.125 + -10.875

Combine like terms: 10.875 + -10.875 = 0.000
0.000 + x = -10.125 + -10.875
x = -10.125 + -10.875

Combine like terms: -10.125 + -10.875 = -21
x = -21

Simplifying
x = -21


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.75, -21}

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