119x^2+30x-4=0

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Solution for 119x^2+30x-4=0 equation:


Simplifying
119x2 + 30x + -4 = 0

Reorder the terms:
-4 + 30x + 119x2 = 0

Solving
-4 + 30x + 119x2 = 0

Solving for variable 'x'.

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

Divide each side by '119'.
-0.03361344538 + 0.2521008403x + x2 = 0

Move the constant term to the right:

Add '0.03361344538' to each side of the equation.
-0.03361344538 + 0.2521008403x + 0.03361344538 + x2 = 0 + 0.03361344538

Reorder the terms:
-0.03361344538 + 0.03361344538 + 0.2521008403x + x2 = 0 + 0.03361344538

Combine like terms: -0.03361344538 + 0.03361344538 = 0.00000000000
0.00000000000 + 0.2521008403x + x2 = 0 + 0.03361344538
0.2521008403x + x2 = 0 + 0.03361344538

Combine like terms: 0 + 0.03361344538 = 0.03361344538
0.2521008403x + x2 = 0.03361344538

The x term is 0.2521008403x.  Take half its coefficient (0.1260504202).
Square it (0.01588870843) and add it to both sides.

Add '0.01588870843' to each side of the equation.
0.2521008403x + 0.01588870843 + x2 = 0.03361344538 + 0.01588870843

Reorder the terms:
0.01588870843 + 0.2521008403x + x2 = 0.03361344538 + 0.01588870843

Combine like terms: 0.03361344538 + 0.01588870843 = 0.04950215381
0.01588870843 + 0.2521008403x + x2 = 0.04950215381

Factor a perfect square on the left side:
(x + 0.1260504202)(x + 0.1260504202) = 0.04950215381

Calculate the square root of the right side: 0.222490795

Break this problem into two subproblems by setting 
(x + 0.1260504202) equal to 0.222490795 and -0.222490795.

Subproblem 1

x + 0.1260504202 = 0.222490795 Simplifying x + 0.1260504202 = 0.222490795 Reorder the terms: 0.1260504202 + x = 0.222490795 Solving 0.1260504202 + x = 0.222490795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1260504202' to each side of the equation. 0.1260504202 + -0.1260504202 + x = 0.222490795 + -0.1260504202 Combine like terms: 0.1260504202 + -0.1260504202 = 0.0000000000 0.0000000000 + x = 0.222490795 + -0.1260504202 x = 0.222490795 + -0.1260504202 Combine like terms: 0.222490795 + -0.1260504202 = 0.0964403748 x = 0.0964403748 Simplifying x = 0.0964403748

Subproblem 2

x + 0.1260504202 = -0.222490795 Simplifying x + 0.1260504202 = -0.222490795 Reorder the terms: 0.1260504202 + x = -0.222490795 Solving 0.1260504202 + x = -0.222490795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1260504202' to each side of the equation. 0.1260504202 + -0.1260504202 + x = -0.222490795 + -0.1260504202 Combine like terms: 0.1260504202 + -0.1260504202 = 0.0000000000 0.0000000000 + x = -0.222490795 + -0.1260504202 x = -0.222490795 + -0.1260504202 Combine like terms: -0.222490795 + -0.1260504202 = -0.3485412152 x = -0.3485412152 Simplifying x = -0.3485412152

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.0964403748, -0.3485412152}

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