0.08x^2+1.6x-16=0

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Solution for 0.08x^2+1.6x-16=0 equation:


Simplifying
0.08x2 + 1.6x + -16 = 0

Reorder the terms:
-16 + 1.6x + 0.08x2 = 0

Solving
-16 + 1.6x + 0.08x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.08'.
-200 + 20x + x2 = 0

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 20x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 20x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 20x + x2 = 0 + 200
20x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
20x + x2 = 200

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 200 + 100

Reorder the terms:
100 + 20x + x2 = 200 + 100

Combine like terms: 200 + 100 = 300
100 + 20x + x2 = 300

Factor a perfect square on the left side:
(x + 10)(x + 10) = 300

Calculate the square root of the right side: 17.320508076

Break this problem into two subproblems by setting 
(x + 10) equal to 17.320508076 and -17.320508076.

Subproblem 1

x + 10 = 17.320508076 Simplifying x + 10 = 17.320508076 Reorder the terms: 10 + x = 17.320508076 Solving 10 + x = 17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 17.320508076 + -10 Combine like terms: 10 + -10 = 0 0 + x = 17.320508076 + -10 x = 17.320508076 + -10 Combine like terms: 17.320508076 + -10 = 7.320508076 x = 7.320508076 Simplifying x = 7.320508076

Subproblem 2

x + 10 = -17.320508076 Simplifying x + 10 = -17.320508076 Reorder the terms: 10 + x = -17.320508076 Solving 10 + x = -17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -17.320508076 + -10 Combine like terms: 10 + -10 = 0 0 + x = -17.320508076 + -10 x = -17.320508076 + -10 Combine like terms: -17.320508076 + -10 = -27.320508076 x = -27.320508076 Simplifying x = -27.320508076

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.320508076, -27.320508076}

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