-0.083333x^2-2x+32=0

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Solution for -0.083333x^2-2x+32=0 equation:


Simplifying
-0.083333x2 + -2x + 32 = 0

Reorder the terms:
32 + -2x + -0.083333x2 = 0

Solving
32 + -2x + -0.083333x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.083333 the coefficient of the squared term: 

Divide each side by '-0.083333'.
-384.001536 + 24.000096x + x2 = 0

Move the constant term to the right:

Add '384.001536' to each side of the equation.
-384.001536 + 24.000096x + 384.001536 + x2 = 0 + 384.001536

Reorder the terms:
-384.001536 + 384.001536 + 24.000096x + x2 = 0 + 384.001536

Combine like terms: -384.001536 + 384.001536 = 0.000000
0.000000 + 24.000096x + x2 = 0 + 384.001536
24.000096x + x2 = 0 + 384.001536

Combine like terms: 0 + 384.001536 = 384.001536
24.000096x + x2 = 384.001536

The x term is 24.000096x.  Take half its coefficient (12.000048).
Square it (144.0011520) and add it to both sides.

Add '144.0011520' to each side of the equation.
24.000096x + 144.0011520 + x2 = 384.001536 + 144.0011520

Reorder the terms:
144.0011520 + 24.000096x + x2 = 384.001536 + 144.0011520

Combine like terms: 384.001536 + 144.0011520 = 528.002688
144.0011520 + 24.000096x + x2 = 528.002688

Factor a perfect square on the left side:
(x + 12.000048)(x + 12.000048) = 528.002688

Calculate the square root of the right side: 22.978309076

Break this problem into two subproblems by setting 
(x + 12.000048) equal to 22.978309076 and -22.978309076.

Subproblem 1

x + 12.000048 = 22.978309076 Simplifying x + 12.000048 = 22.978309076 Reorder the terms: 12.000048 + x = 22.978309076 Solving 12.000048 + x = 22.978309076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.000048' to each side of the equation. 12.000048 + -12.000048 + x = 22.978309076 + -12.000048 Combine like terms: 12.000048 + -12.000048 = 0.000000 0.000000 + x = 22.978309076 + -12.000048 x = 22.978309076 + -12.000048 Combine like terms: 22.978309076 + -12.000048 = 10.978261076 x = 10.978261076 Simplifying x = 10.978261076

Subproblem 2

x + 12.000048 = -22.978309076 Simplifying x + 12.000048 = -22.978309076 Reorder the terms: 12.000048 + x = -22.978309076 Solving 12.000048 + x = -22.978309076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.000048' to each side of the equation. 12.000048 + -12.000048 + x = -22.978309076 + -12.000048 Combine like terms: 12.000048 + -12.000048 = 0.000000 0.000000 + x = -22.978309076 + -12.000048 x = -22.978309076 + -12.000048 Combine like terms: -22.978309076 + -12.000048 = -34.978357076 x = -34.978357076 Simplifying x = -34.978357076

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.978261076, -34.978357076}

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