.012x^2-.1x+.18=0

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Solution for .012x^2-.1x+.18=0 equation:


Simplifying
0.012x2 + -0.1x + 0.18 = 0

Reorder the terms:
0.18 + -0.1x + 0.012x2 = 0

Solving
0.18 + -0.1x + 0.012x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.012'.
15 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -8.333333333x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -8.333333333x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -8.333333333x + x2 = 0 + -15
-8.333333333x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-8.333333333x + x2 = -15

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -15 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -15 + 17.36111111

Combine like terms: -15 + 17.36111111 = 2.36111111
17.36111111 + -8.333333333x + x2 = 2.36111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 2.36111111

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 1.536590743 and -1.536590743.

Subproblem 1

x + -4.166666667 = 1.536590743 Simplifying x + -4.166666667 = 1.536590743 Reorder the terms: -4.166666667 + x = 1.536590743 Solving -4.166666667 + x = 1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 1.536590743 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 1.536590743 + 4.166666667 x = 1.536590743 + 4.166666667 Combine like terms: 1.536590743 + 4.166666667 = 5.70325741 x = 5.70325741 Simplifying x = 5.70325741

Subproblem 2

x + -4.166666667 = -1.536590743 Simplifying x + -4.166666667 = -1.536590743 Reorder the terms: -4.166666667 + x = -1.536590743 Solving -4.166666667 + x = -1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -1.536590743 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -1.536590743 + 4.166666667 x = -1.536590743 + 4.166666667 Combine like terms: -1.536590743 + 4.166666667 = 2.630075924 x = 2.630075924 Simplifying x = 2.630075924

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.70325741, 2.630075924}

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