x^2+5x=47.75

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Solution for x^2+5x=47.75 equation: 


Simplifying
x2 + 5x = 47.75

Reorder the terms:
5x + x2 = 47.75

Solving
5x + x2 = 47.75

Solving for variable 'x'.

Reorder the terms:
-47.75 + 5x + x2 = 47.75 + -47.75

Combine like terms: 47.75 + -47.75 = 0.00
-47.75 + 5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '47.75' to each side of the equation.
-47.75 + 5x + 47.75 + x2 = 0.00 + 47.75

Reorder the terms:
-47.75 + 47.75 + 5x + x2 = 0.00 + 47.75

Combine like terms: -47.75 + 47.75 = 0.00
0.00 + 5x + x2 = 0.00 + 47.75
5x + x2 = 0.00 + 47.75

Combine like terms: 0.00 + 47.75 = 47.75
5x + x2 = 47.75

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 = 47.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 47.75 + 6.25

Combine like terms: 47.75 + 6.25 = 54
6.25 + 5x + x2 = 54

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.348469228 and -7.348469228.


Subproblem 1
x + 2.5 = 7.348469228

Simplifying
x + 2.5 = 7.348469228

Reorder the terms:
2.5 + x = 7.348469228

Solving
2.5 + x = 7.348469228

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 = 7.348469228 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.348469228 + -2.5
x = 7.348469228 + -2.5

Combine like terms: 7.348469228 + -2.5 = 4.848469228
x = 4.848469228

Simplifying
x = 4.848469228


Subproblem 2
x + 2.5 = -7.348469228

Simplifying
x + 2.5 = -7.348469228

Reorder the terms:
2.5 + x = -7.348469228

Solving
2.5 + x = -7.348469228

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 = -7.348469228 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.348469228 + -2.5
x = -7.348469228 + -2.5

Combine like terms: -7.348469228 + -2.5 = -9.848469228
x = -9.848469228

Simplifying
x = -9.848469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.848469228, -9.848469228}

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