3x^2+36x-10=0

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Solution for 3x^2+36x-10=0 equation:


Simplifying
3x2 + 36x + -10 = 0

Reorder the terms:
-10 + 36x + 3x2 = 0

Solving
-10 + 36x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-3.333333333 + 12x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 12x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 12x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 12x + x2 = 0 + 3.333333333
12x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
12x + x2 = 3.333333333

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 3.333333333 + 36

Reorder the terms:
36 + 12x + x2 = 3.333333333 + 36

Combine like terms: 3.333333333 + 36 = 39.333333333
36 + 12x + x2 = 39.333333333

Factor a perfect square on the left side:
(x + 6)(x + 6) = 39.333333333

Calculate the square root of the right side: 6.271629241

Break this problem into two subproblems by setting 
(x + 6) equal to 6.271629241 and -6.271629241.

Subproblem 1

x + 6 = 6.271629241 Simplifying x + 6 = 6.271629241 Reorder the terms: 6 + x = 6.271629241 Solving 6 + x = 6.271629241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.271629241 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.271629241 + -6 x = 6.271629241 + -6 Combine like terms: 6.271629241 + -6 = 0.271629241 x = 0.271629241 Simplifying x = 0.271629241

Subproblem 2

x + 6 = -6.271629241 Simplifying x + 6 = -6.271629241 Reorder the terms: 6 + x = -6.271629241 Solving 6 + x = -6.271629241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.271629241 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.271629241 + -6 x = -6.271629241 + -6 Combine like terms: -6.271629241 + -6 = -12.271629241 x = -12.271629241 Simplifying x = -12.271629241

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.271629241, -12.271629241}

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