0=x^2+15x+178.75

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Solution for 0=x^2+15x+178.75 equation: 


Simplifying
0 = x2 + 15x + 178.75

Reorder the terms:
0 = 178.75 + 15x + x2

Solving
0 = 178.75 + 15x + x2

Solving for variable 'x'.

Combine like terms: 0 + -178.75 = -178.75
-178.75 + -15x + -1x2 = 178.75 + 15x + x2 + -178.75 + -15x + -1x2

Reorder the terms:
-178.75 + -15x + -1x2 = 178.75 + -178.75 + 15x + -15x + x2 + -1x2

Combine like terms: 178.75 + -178.75 = 0.00
-178.75 + -15x + -1x2 = 0.00 + 15x + -15x + x2 + -1x2
-178.75 + -15x + -1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
-178.75 + -15x + -1x2 = 0 + x2 + -1x2
-178.75 + -15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-178.75 + -15x + -1x2 = 0

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

Divide each side by '-1'.
178.75 + 15x + x2 = 0

Move the constant term to the right:

Add '-178.75' to each side of the equation.
178.75 + 15x + -178.75 + x2 = 0 + -178.75

Reorder the terms:
178.75 + -178.75 + 15x + x2 = 0 + -178.75

Combine like terms: 178.75 + -178.75 = 0.00
0.00 + 15x + x2 = 0 + -178.75
15x + x2 = 0 + -178.75

Combine like terms: 0 + -178.75 = -178.75
15x + x2 = -178.75

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -178.75 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -178.75 + 56.25

Combine like terms: -178.75 + 56.25 = -122.5
56.25 + 15x + x2 = -122.5

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = -122.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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