-6x=0.5x^2-16

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Solution for -6x=0.5x^2-16 equation:


Simplifying
-6x = 0.5x2 + -16

Reorder the terms:
-6x = -16 + 0.5x2

Solving
-6x = -16 + 0.5x2

Solving for variable 'x'.

Reorder the terms:
16 + -6x + -0.5x2 = -16 + 0.5x2 + 16 + -0.5x2

Reorder the terms:
16 + -6x + -0.5x2 = -16 + 16 + 0.5x2 + -0.5x2

Combine like terms: -16 + 16 = 0
16 + -6x + -0.5x2 = 0 + 0.5x2 + -0.5x2
16 + -6x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
16 + -6x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-32 + 12x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 12x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 12x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 12x + x2 = 0 + 32
12x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
12x + x2 = 32

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 32 + 36

Reorder the terms:
36 + 12x + x2 = 32 + 36

Combine like terms: 32 + 36 = 68
36 + 12x + x2 = 68

Factor a perfect square on the left side:
(x + 6)(x + 6) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(x + 6) equal to 8.246211251 and -8.246211251.

Subproblem 1

x + 6 = 8.246211251 Simplifying x + 6 = 8.246211251 Reorder the terms: 6 + x = 8.246211251 Solving 6 + x = 8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.246211251 + -6 x = 8.246211251 + -6 Combine like terms: 8.246211251 + -6 = 2.246211251 x = 2.246211251 Simplifying x = 2.246211251

Subproblem 2

x + 6 = -8.246211251 Simplifying x + 6 = -8.246211251 Reorder the terms: 6 + x = -8.246211251 Solving 6 + x = -8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.246211251 + -6 x = -8.246211251 + -6 Combine like terms: -8.246211251 + -6 = -14.246211251 x = -14.246211251 Simplifying x = -14.246211251

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.246211251, -14.246211251}

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