-630.75+47.5x+x^2=0

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Solution for -630.75+47.5x+x^2=0 equation: 


Simplifying
-630.75 + 47.5x + x2 = 0

Solving
-630.75 + 47.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '630.75' to each side of the equation.
-630.75 + 47.5x + 630.75 + x2 = 0 + 630.75

Reorder the terms:
-630.75 + 630.75 + 47.5x + x2 = 0 + 630.75

Combine like terms: -630.75 + 630.75 = 0.00
0.00 + 47.5x + x2 = 0 + 630.75
47.5x + x2 = 0 + 630.75

Combine like terms: 0 + 630.75 = 630.75
47.5x + x2 = 630.75

The x term is 47.5x.  Take half its coefficient (23.75).
Square it (564.0625) and add it to both sides.

Add '564.0625' to each side of the equation.
47.5x + 564.0625 + x2 = 630.75 + 564.0625

Reorder the terms:
564.0625 + 47.5x + x2 = 630.75 + 564.0625

Combine like terms: 630.75 + 564.0625 = 1194.8125
564.0625 + 47.5x + x2 = 1194.8125

Factor a perfect square on the left side:
(x + 23.75)(x + 23.75) = 1194.8125

Calculate the square root of the right side: 34.566059943

Break this problem into two subproblems by setting 
(x + 23.75) equal to 34.566059943 and -34.566059943.


Subproblem 1
x + 23.75 = 34.566059943

Simplifying
x + 23.75 = 34.566059943

Reorder the terms:
23.75 + x = 34.566059943

Solving
23.75 + x = 34.566059943

Solving for variable 'x'.

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

Add '-23.75' to each side of the equation.
23.75 + -23.75 + x = 34.566059943 + -23.75

Combine like terms: 23.75 + -23.75 = 0.00
0.00 + x = 34.566059943 + -23.75
x = 34.566059943 + -23.75

Combine like terms: 34.566059943 + -23.75 = 10.816059943
x = 10.816059943

Simplifying
x = 10.816059943


Subproblem 2
x + 23.75 = -34.566059943

Simplifying
x + 23.75 = -34.566059943

Reorder the terms:
23.75 + x = -34.566059943

Solving
23.75 + x = -34.566059943

Solving for variable 'x'.

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

Add '-23.75' to each side of the equation.
23.75 + -23.75 + x = -34.566059943 + -23.75

Combine like terms: 23.75 + -23.75 = 0.00
0.00 + x = -34.566059943 + -23.75
x = -34.566059943 + -23.75

Combine like terms: -34.566059943 + -23.75 = -58.316059943
x = -58.316059943

Simplifying
x = -58.316059943


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.816059943, -58.316059943}

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