35x^2+2x-12=0

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Solution for 35x^2+2x-12=0 equation:


Simplifying
35x2 + 2x + -12 = 0

Reorder the terms:
-12 + 2x + 35x2 = 0

Solving
-12 + 2x + 35x2 = 0

Solving for variable 'x'.

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

Divide each side by '35'.
-0.3428571429 + 0.05714285714x + x2 = 0

Move the constant term to the right:

Add '0.3428571429' to each side of the equation.
-0.3428571429 + 0.05714285714x + 0.3428571429 + x2 = 0 + 0.3428571429

Reorder the terms:
-0.3428571429 + 0.3428571429 + 0.05714285714x + x2 = 0 + 0.3428571429

Combine like terms: -0.3428571429 + 0.3428571429 = 0.0000000000
0.0000000000 + 0.05714285714x + x2 = 0 + 0.3428571429
0.05714285714x + x2 = 0 + 0.3428571429

Combine like terms: 0 + 0.3428571429 = 0.3428571429
0.05714285714x + x2 = 0.3428571429

The x term is 0.05714285714x.  Take half its coefficient (0.02857142857).
Square it (0.0008163265305) and add it to both sides.

Add '0.0008163265305' to each side of the equation.
0.05714285714x + 0.0008163265305 + x2 = 0.3428571429 + 0.0008163265305

Reorder the terms:
0.0008163265305 + 0.05714285714x + x2 = 0.3428571429 + 0.0008163265305

Combine like terms: 0.3428571429 + 0.0008163265305 = 0.3436734694305
0.0008163265305 + 0.05714285714x + x2 = 0.3436734694305

Factor a perfect square on the left side:
(x + 0.02857142857)(x + 0.02857142857) = 0.3436734694305

Calculate the square root of the right side: 0.586236701

Break this problem into two subproblems by setting 
(x + 0.02857142857) equal to 0.586236701 and -0.586236701.

Subproblem 1

x + 0.02857142857 = 0.586236701 Simplifying x + 0.02857142857 = 0.586236701 Reorder the terms: 0.02857142857 + x = 0.586236701 Solving 0.02857142857 + x = 0.586236701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02857142857' to each side of the equation. 0.02857142857 + -0.02857142857 + x = 0.586236701 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + x = 0.586236701 + -0.02857142857 x = 0.586236701 + -0.02857142857 Combine like terms: 0.586236701 + -0.02857142857 = 0.55766527243 x = 0.55766527243 Simplifying x = 0.55766527243

Subproblem 2

x + 0.02857142857 = -0.586236701 Simplifying x + 0.02857142857 = -0.586236701 Reorder the terms: 0.02857142857 + x = -0.586236701 Solving 0.02857142857 + x = -0.586236701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02857142857' to each side of the equation. 0.02857142857 + -0.02857142857 + x = -0.586236701 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + x = -0.586236701 + -0.02857142857 x = -0.586236701 + -0.02857142857 Combine like terms: -0.586236701 + -0.02857142857 = -0.61480812957 x = -0.61480812957 Simplifying x = -0.61480812957

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.55766527243, -0.61480812957}

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