0=x*x+2.5x-16.5

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Solution for 0=x*x+2.5x-16.5 equation: 


Simplifying
0 = x * x + 2.5x + -16.5

Multiply x * x
0 = x2 + 2.5x + -16.5

Reorder the terms:
0 = -16.5 + 2.5x + x2

Solving
0 = -16.5 + 2.5x + x2

Solving for variable 'x'.

Combine like terms: 0 + 16.5 = 16.5
16.5 + -2.5x + -1x2 = -16.5 + 2.5x + x2 + 16.5 + -2.5x + -1x2

Reorder the terms:
16.5 + -2.5x + -1x2 = -16.5 + 16.5 + 2.5x + -2.5x + x2 + -1x2

Combine like terms: -16.5 + 16.5 = 0.0
16.5 + -2.5x + -1x2 = 0.0 + 2.5x + -2.5x + x2 + -1x2
16.5 + -2.5x + -1x2 = 2.5x + -2.5x + x2 + -1x2

Combine like terms: 2.5x + -2.5x = 0.0
16.5 + -2.5x + -1x2 = 0.0 + x2 + -1x2
16.5 + -2.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16.5 + -2.5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + 2.5x + 16.5 + x2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + 2.5x + x2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + 2.5x + x2 = 0 + 16.5
2.5x + x2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
2.5x + x2 = 16.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 16.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 16.5 + 1.5625

Combine like terms: 16.5 + 1.5625 = 18.0625
1.5625 + 2.5x + x2 = 18.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 18.0625

Calculate the square root of the right side: 4.25

Break this problem into two subproblems by setting 
(x + 1.25) equal to 4.25 and -4.25.


Subproblem 1
x + 1.25 = 4.25

Simplifying
x + 1.25 = 4.25

Reorder the terms:
1.25 + x = 4.25

Solving
1.25 + x = 4.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 4.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 4.25 + -1.25
x = 4.25 + -1.25

Combine like terms: 4.25 + -1.25 = 3
x = 3

Simplifying
x = 3


Subproblem 2
x + 1.25 = -4.25

Simplifying
x + 1.25 = -4.25

Reorder the terms:
1.25 + x = -4.25

Solving
1.25 + x = -4.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -4.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -4.25 + -1.25
x = -4.25 + -1.25

Combine like terms: -4.25 + -1.25 = -5.5
x = -5.5

Simplifying
x = -5.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, -5.5}

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