.5(x-48)=12+5x^2

Solution for .5(x-48)=12+5x^2 equation:

Simplifying
0.5(x + -48) = 12 + 5x2

Reorder the terms:
0.5(-48 + x) = 12 + 5x2
(-48 * 0.5 + x * 0.5) = 12 + 5x2
(-24 + 0.5x) = 12 + 5x2

Solving
-24 + 0.5x = 12 + 5x2

Solving for variable 'x'.

Reorder the terms:
-24 + -12 + 0.5x + -5x2 = 12 + 5x2 + -12 + -5x2

Combine like terms: -24 + -12 = -36
-36 + 0.5x + -5x2 = 12 + 5x2 + -12 + -5x2

Reorder the terms:
-36 + 0.5x + -5x2 = 12 + -12 + 5x2 + -5x2

Combine like terms: 12 + -12 = 0
-36 + 0.5x + -5x2 = 0 + 5x2 + -5x2
-36 + 0.5x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-36 + 0.5x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
7.2 + -0.1x + x2 = 0

Move the constant term to the right:

Add '-7.2' to each side of the equation.
7.2 + -0.1x + -7.2 + x2 = 0 + -7.2

Reorder the terms:
7.2 + -7.2 + -0.1x + x2 = 0 + -7.2

Combine like terms: 7.2 + -7.2 = 0.0
0.0 + -0.1x + x2 = 0 + -7.2
-0.1x + x2 = 0 + -7.2

Combine like terms: 0 + -7.2 = -7.2
-0.1x + x2 = -7.2

The x term is -0.1x.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x + 0.0025 + x2 = -7.2 + 0.0025

Reorder the terms:
0.0025 + -0.1x + x2 = -7.2 + 0.0025

Combine like terms: -7.2 + 0.0025 = -7.1975
0.0025 + -0.1x + x2 = -7.1975

Factor a perfect square on the left side:
(x + -0.05)(x + -0.05) = -7.1975

Can't calculate square root of the right side.

The solution to this equation could not be determined.