0.5x+6=x^2+12x

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Solution for 0.5x+6=x^2+12x equation:


Simplifying
0.5x + 6 = x2 + 12x

Reorder the terms:
6 + 0.5x = x2 + 12x

Reorder the terms:
6 + 0.5x = 12x + x2

Solving
6 + 0.5x = 12x + x2

Solving for variable 'x'.

Combine like terms: 0.5x + -12x = -11.5x
6 + -11.5x + -1x2 = 12x + x2 + -12x + -1x2

Reorder the terms:
6 + -11.5x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
6 + -11.5x + -1x2 = 0 + x2 + -1x2
6 + -11.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -11.5x + -1x2 = 0

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

Divide each side by '-1'.
-6 + 11.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 11.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 11.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 11.5x + x2 = 0 + 6
11.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
11.5x + x2 = 6

The x term is 11.5x.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5x + 33.0625 + x2 = 6 + 33.0625

Reorder the terms:
33.0625 + 11.5x + x2 = 6 + 33.0625

Combine like terms: 6 + 33.0625 = 39.0625
33.0625 + 11.5x + x2 = 39.0625

Factor a perfect square on the left side:
(x + 5.75)(x + 5.75) = 39.0625

Calculate the square root of the right side: 6.25

Break this problem into two subproblems by setting 
(x + 5.75) equal to 6.25 and -6.25.

Subproblem 1

x + 5.75 = 6.25 Simplifying x + 5.75 = 6.25 Reorder the terms: 5.75 + x = 6.25 Solving 5.75 + x = 6.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 6.25 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 6.25 + -5.75 x = 6.25 + -5.75 Combine like terms: 6.25 + -5.75 = 0.5 x = 0.5 Simplifying x = 0.5

Subproblem 2

x + 5.75 = -6.25 Simplifying x + 5.75 = -6.25 Reorder the terms: 5.75 + x = -6.25 Solving 5.75 + x = -6.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -6.25 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -6.25 + -5.75 x = -6.25 + -5.75 Combine like terms: -6.25 + -5.75 = -12 x = -12 Simplifying x = -12

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5, -12}

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