0.0000987x^2-0.0122x+0.0613=0

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Solution for 0.0000987x^2-0.0122x+0.0613=0 equation:


Simplifying
0.0000987x2 + -0.0122x + 0.0613 = 0

Reorder the terms:
0.0613 + -0.0122x + 0.0000987x2 = 0

Solving
0.0613 + -0.0122x + 0.0000987x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0000987 the coefficient of the squared term: 

Divide each side by '0.0000987'.
621.0739615 + -123.6068896x + x2 = 0

Move the constant term to the right:

Add '-621.0739615' to each side of the equation.
621.0739615 + -123.6068896x + -621.0739615 + x2 = 0 + -621.0739615

Reorder the terms:
621.0739615 + -621.0739615 + -123.6068896x + x2 = 0 + -621.0739615

Combine like terms: 621.0739615 + -621.0739615 = 0.0000000
0.0000000 + -123.6068896x + x2 = 0 + -621.0739615
-123.6068896x + x2 = 0 + -621.0739615

Combine like terms: 0 + -621.0739615 = -621.0739615
-123.6068896x + x2 = -621.0739615

The x term is -123.6068896x.  Take half its coefficient (-61.8034448).
Square it (3819.665789) and add it to both sides.

Add '3819.665789' to each side of the equation.
-123.6068896x + 3819.665789 + x2 = -621.0739615 + 3819.665789

Reorder the terms:
3819.665789 + -123.6068896x + x2 = -621.0739615 + 3819.665789

Combine like terms: -621.0739615 + 3819.665789 = 3198.5918275
3819.665789 + -123.6068896x + x2 = 3198.5918275

Factor a perfect square on the left side:
(x + -61.8034448)(x + -61.8034448) = 3198.5918275

Calculate the square root of the right side: 56.556094521

Break this problem into two subproblems by setting 
(x + -61.8034448) equal to 56.556094521 and -56.556094521.

Subproblem 1

x + -61.8034448 = 56.556094521 Simplifying x + -61.8034448 = 56.556094521 Reorder the terms: -61.8034448 + x = 56.556094521 Solving -61.8034448 + x = 56.556094521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.8034448' to each side of the equation. -61.8034448 + 61.8034448 + x = 56.556094521 + 61.8034448 Combine like terms: -61.8034448 + 61.8034448 = 0.0000000 0.0000000 + x = 56.556094521 + 61.8034448 x = 56.556094521 + 61.8034448 Combine like terms: 56.556094521 + 61.8034448 = 118.359539321 x = 118.359539321 Simplifying x = 118.359539321

Subproblem 2

x + -61.8034448 = -56.556094521 Simplifying x + -61.8034448 = -56.556094521 Reorder the terms: -61.8034448 + x = -56.556094521 Solving -61.8034448 + x = -56.556094521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61.8034448' to each side of the equation. -61.8034448 + 61.8034448 + x = -56.556094521 + 61.8034448 Combine like terms: -61.8034448 + 61.8034448 = 0.0000000 0.0000000 + x = -56.556094521 + 61.8034448 x = -56.556094521 + 61.8034448 Combine like terms: -56.556094521 + 61.8034448 = 5.247350279 x = 5.247350279 Simplifying x = 5.247350279

Solution

The solution to the problem is based on the solutions from the subproblems. x = {118.359539321, 5.247350279}

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