x^2+5*x-141.25=

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Solution for x^2+5*x-141.25= equation: 


Simplifying
x2 + 5x + -141.25 = 0

Reorder the terms:
-141.25 + 5x + x2 = 0

Solving
-141.25 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '141.25' to each side of the equation.
-141.25 + 5x + 141.25 + x2 = 0 + 141.25

Reorder the terms:
-141.25 + 141.25 + 5x + x2 = 0 + 141.25

Combine like terms: -141.25 + 141.25 = 0.00
0.00 + 5x + x2 = 0 + 141.25
5x + x2 = 0 + 141.25

Combine like terms: 0 + 141.25 = 141.25
5x + x2 = 141.25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 141.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 141.25 + 6.25

Combine like terms: 141.25 + 6.25 = 147.5
6.25 + 5x + x2 = 147.5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 147.5

Calculate the square root of the right side: 12.144957801

Break this problem into two subproblems by setting 
(x + 2.5) equal to 12.144957801 and -12.144957801.


Subproblem 1
x + 2.5 = 12.144957801

Simplifying
x + 2.5 = 12.144957801

Reorder the terms:
2.5 + x = 12.144957801

Solving
2.5 + x = 12.144957801

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 12.144957801 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 12.144957801 + -2.5
x = 12.144957801 + -2.5

Combine like terms: 12.144957801 + -2.5 = 9.644957801
x = 9.644957801

Simplifying
x = 9.644957801


Subproblem 2
x + 2.5 = -12.144957801

Simplifying
x + 2.5 = -12.144957801

Reorder the terms:
2.5 + x = -12.144957801

Solving
2.5 + x = -12.144957801

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -12.144957801 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -12.144957801 + -2.5
x = -12.144957801 + -2.5

Combine like terms: -12.144957801 + -2.5 = -14.644957801
x = -14.644957801

Simplifying
x = -14.644957801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.644957801, -14.644957801}

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