x^2+2.5x=31.5

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Solution for x^2+2.5x=31.5 equation: 


Simplifying
x2 + 2.5x = 31.5

Reorder the terms:
2.5x + x2 = 31.5

Solving
2.5x + x2 = 31.5

Solving for variable 'x'.

Reorder the terms:
-31.5 + 2.5x + x2 = 31.5 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
-31.5 + 2.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + 2.5x + 31.5 + x2 = 0.0 + 31.5

Reorder the terms:
-31.5 + 31.5 + 2.5x + x2 = 0.0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + 2.5x + x2 = 0.0 + 31.5
2.5x + x2 = 0.0 + 31.5

Combine like terms: 0.0 + 31.5 = 31.5
2.5x + x2 = 31.5

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 = 31.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 31.5 + 1.5625

Combine like terms: 31.5 + 1.5625 = 33.0625
1.5625 + 2.5x + x2 = 33.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 33.0625

Calculate the square root of the right side: 5.75

Break this problem into two subproblems by setting 
(x + 1.25) equal to 5.75 and -5.75.


Subproblem 1
x + 1.25 = 5.75

Simplifying
x + 1.25 = 5.75

Reorder the terms:
1.25 + x = 5.75

Solving
1.25 + x = 5.75

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 = 5.75 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 5.75 + -1.25
x = 5.75 + -1.25

Combine like terms: 5.75 + -1.25 = 4.5
x = 4.5

Simplifying
x = 4.5


Subproblem 2
x + 1.25 = -5.75

Simplifying
x + 1.25 = -5.75

Reorder the terms:
1.25 + x = -5.75

Solving
1.25 + x = -5.75

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 = -5.75 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -5.75 + -1.25
x = -5.75 + -1.25

Combine like terms: -5.75 + -1.25 = -7
x = -7

Simplifying
x = -7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5, -7}

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