.009x^2+.08x+.16=0

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Solution for .009x^2+.08x+.16=0 equation:


Simplifying
0.009x2 + 0.08x + 0.16 = 0

Reorder the terms:
0.16 + 0.08x + 0.009x2 = 0

Solving
0.16 + 0.08x + 0.009x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.009'.
17.77777778 + 8.888888889x + x2 = 0

Move the constant term to the right:

Add '-17.77777778' to each side of the equation.
17.77777778 + 8.888888889x + -17.77777778 + x2 = 0 + -17.77777778

Reorder the terms:
17.77777778 + -17.77777778 + 8.888888889x + x2 = 0 + -17.77777778

Combine like terms: 17.77777778 + -17.77777778 = 0.00000000
0.00000000 + 8.888888889x + x2 = 0 + -17.77777778
8.888888889x + x2 = 0 + -17.77777778

Combine like terms: 0 + -17.77777778 = -17.77777778
8.888888889x + x2 = -17.77777778

The x term is 8.888888889x.  Take half its coefficient (4.444444445).
Square it (19.75308642) and add it to both sides.

Add '19.75308642' to each side of the equation.
8.888888889x + 19.75308642 + x2 = -17.77777778 + 19.75308642

Reorder the terms:
19.75308642 + 8.888888889x + x2 = -17.77777778 + 19.75308642

Combine like terms: -17.77777778 + 19.75308642 = 1.97530864
19.75308642 + 8.888888889x + x2 = 1.97530864

Factor a perfect square on the left side:
(x + 4.444444445)(x + 4.444444445) = 1.97530864

Calculate the square root of the right side: 1.405456737

Break this problem into two subproblems by setting 
(x + 4.444444445) equal to 1.405456737 and -1.405456737.

Subproblem 1

x + 4.444444445 = 1.405456737 Simplifying x + 4.444444445 = 1.405456737 Reorder the terms: 4.444444445 + x = 1.405456737 Solving 4.444444445 + x = 1.405456737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.444444445' to each side of the equation. 4.444444445 + -4.444444445 + x = 1.405456737 + -4.444444445 Combine like terms: 4.444444445 + -4.444444445 = 0.000000000 0.000000000 + x = 1.405456737 + -4.444444445 x = 1.405456737 + -4.444444445 Combine like terms: 1.405456737 + -4.444444445 = -3.038987708 x = -3.038987708 Simplifying x = -3.038987708

Subproblem 2

x + 4.444444445 = -1.405456737 Simplifying x + 4.444444445 = -1.405456737 Reorder the terms: 4.444444445 + x = -1.405456737 Solving 4.444444445 + x = -1.405456737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.444444445' to each side of the equation. 4.444444445 + -4.444444445 + x = -1.405456737 + -4.444444445 Combine like terms: 4.444444445 + -4.444444445 = 0.000000000 0.000000000 + x = -1.405456737 + -4.444444445 x = -1.405456737 + -4.444444445 Combine like terms: -1.405456737 + -4.444444445 = -5.849901182 x = -5.849901182 Simplifying x = -5.849901182

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.038987708, -5.849901182}

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