30x^2+26x+3=0

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Solution for 30x^2+26x+3=0 equation:


Simplifying
30x2 + 26x + 3 = 0

Reorder the terms:
3 + 26x + 30x2 = 0

Solving
3 + 26x + 30x2 = 0

Solving for variable 'x'.

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

Divide each side by '30'.
0.1 + 0.8666666667x + x2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + 0.8666666667x + -0.1 + x2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + 0.8666666667x + x2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + 0.8666666667x + x2 = 0 + -0.1
0.8666666667x + x2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
0.8666666667x + x2 = -0.1

The x term is 0.8666666667x.  Take half its coefficient (0.4333333334).
Square it (0.1877777778) and add it to both sides.

Add '0.1877777778' to each side of the equation.
0.8666666667x + 0.1877777778 + x2 = -0.1 + 0.1877777778

Reorder the terms:
0.1877777778 + 0.8666666667x + x2 = -0.1 + 0.1877777778

Combine like terms: -0.1 + 0.1877777778 = 0.0877777778
0.1877777778 + 0.8666666667x + x2 = 0.0877777778

Factor a perfect square on the left side:
(x + 0.4333333334)(x + 0.4333333334) = 0.0877777778

Calculate the square root of the right side: 0.296273147

Break this problem into two subproblems by setting 
(x + 0.4333333334) equal to 0.296273147 and -0.296273147.

Subproblem 1

x + 0.4333333334 = 0.296273147 Simplifying x + 0.4333333334 = 0.296273147 Reorder the terms: 0.4333333334 + x = 0.296273147 Solving 0.4333333334 + x = 0.296273147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4333333334' to each side of the equation. 0.4333333334 + -0.4333333334 + x = 0.296273147 + -0.4333333334 Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000 0.0000000000 + x = 0.296273147 + -0.4333333334 x = 0.296273147 + -0.4333333334 Combine like terms: 0.296273147 + -0.4333333334 = -0.1370601864 x = -0.1370601864 Simplifying x = -0.1370601864

Subproblem 2

x + 0.4333333334 = -0.296273147 Simplifying x + 0.4333333334 = -0.296273147 Reorder the terms: 0.4333333334 + x = -0.296273147 Solving 0.4333333334 + x = -0.296273147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4333333334' to each side of the equation. 0.4333333334 + -0.4333333334 + x = -0.296273147 + -0.4333333334 Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000 0.0000000000 + x = -0.296273147 + -0.4333333334 x = -0.296273147 + -0.4333333334 Combine like terms: -0.296273147 + -0.4333333334 = -0.7296064804 x = -0.7296064804 Simplifying x = -0.7296064804

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.1370601864, -0.7296064804}

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