x^2-0.3x+0.0029=0.000000000177

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Solution for x^2-0.3x+0.0029=0.000000000177 equation:


Simplifying
x2 + -0.3x + 0.0029 = 0.000000000177

Reorder the terms:
0.0029 + -0.3x + x2 = 0.000000000177

Solving
0.0029 + -0.3x + x2 = 0.000000000177

Solving for variable 'x'.

Reorder the terms:
0.0029 + -0.000000000177 + -0.3x + x2 = 0.000000000177 + -0.000000000177

Combine like terms: 0.0029 + -0.000000000177 = 0.002899999823
0.002899999823 + -0.3x + x2 = 0.000000000177 + -0.000000000177

Combine like terms: 0.000000000177 + -0.000000000177 = 0.000000000000
0.002899999823 + -0.3x + x2 = 0.000000000000

Begin completing the square.

Move the constant term to the right:

Add '-0.002899999823' to each side of the equation.
0.002899999823 + -0.3x + -0.002899999823 + x2 = 0.000000000000 + -0.002899999823

Reorder the terms:
0.002899999823 + -0.002899999823 + -0.3x + x2 = 0.000000000000 + -0.002899999823

Combine like terms: 0.002899999823 + -0.002899999823 = 0.000000000000
0.000000000000 + -0.3x + x2 = 0.000000000000 + -0.002899999823
-0.3x + x2 = 0.000000000000 + -0.002899999823

Combine like terms: 0.000000000000 + -0.002899999823 = -0.002899999823
-0.3x + x2 = -0.002899999823

The x term is -0.3x.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3x + 0.0225 + x2 = -0.002899999823 + 0.0225

Reorder the terms:
0.0225 + -0.3x + x2 = -0.002899999823 + 0.0225

Combine like terms: -0.002899999823 + 0.0225 = 0.019600000177
0.0225 + -0.3x + x2 = 0.019600000177

Factor a perfect square on the left side:
(x + -0.15)(x + -0.15) = 0.019600000177

Calculate the square root of the right side: 0.140000001

Break this problem into two subproblems by setting 
(x + -0.15) equal to 0.140000001 and -0.140000001.

Subproblem 1

x + -0.15 = 0.140000001 Simplifying x + -0.15 = 0.140000001 Reorder the terms: -0.15 + x = 0.140000001 Solving -0.15 + x = 0.140000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.140000001 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.140000001 + 0.15 x = 0.140000001 + 0.15 Combine like terms: 0.140000001 + 0.15 = 0.290000001 x = 0.290000001 Simplifying x = 0.290000001

Subproblem 2

x + -0.15 = -0.140000001 Simplifying x + -0.15 = -0.140000001 Reorder the terms: -0.15 + x = -0.140000001 Solving -0.15 + x = -0.140000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.140000001 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.140000001 + 0.15 x = -0.140000001 + 0.15 Combine like terms: -0.140000001 + 0.15 = 0.009999999 x = 0.009999999 Simplifying x = 0.009999999

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.290000001, 0.009999999}

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