(6x^2-7x-47)+(9x^2+9x)=

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Solution for (6x^2-7x-47)+(9x^2+9x)= equation:


Simplifying
(6x2 + -7x + -47) + (9x2 + 9x) = 0

Reorder the terms:
(-47 + -7x + 6x2) + (9x2 + 9x) = 0

Remove parenthesis around (-47 + -7x + 6x2)
-47 + -7x + 6x2 + (9x2 + 9x) = 0

Reorder the terms:
-47 + -7x + 6x2 + (9x + 9x2) = 0

Remove parenthesis around (9x + 9x2)
-47 + -7x + 6x2 + 9x + 9x2 = 0

Reorder the terms:
-47 + -7x + 9x + 6x2 + 9x2 = 0

Combine like terms: -7x + 9x = 2x
-47 + 2x + 6x2 + 9x2 = 0

Combine like terms: 6x2 + 9x2 = 15x2
-47 + 2x + 15x2 = 0

Solving
-47 + 2x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-3.133333333 + 0.1333333333x + x2 = 0

Move the constant term to the right:

Add '3.133333333' to each side of the equation.
-3.133333333 + 0.1333333333x + 3.133333333 + x2 = 0 + 3.133333333

Reorder the terms:
-3.133333333 + 3.133333333 + 0.1333333333x + x2 = 0 + 3.133333333

Combine like terms: -3.133333333 + 3.133333333 = 0.000000000
0.000000000 + 0.1333333333x + x2 = 0 + 3.133333333
0.1333333333x + x2 = 0 + 3.133333333

Combine like terms: 0 + 3.133333333 = 3.133333333
0.1333333333x + x2 = 3.133333333

The x term is 0.1333333333x.  Take half its coefficient (0.06666666665).
Square it (0.004444444442) and add it to both sides.

Add '0.004444444442' to each side of the equation.
0.1333333333x + 0.004444444442 + x2 = 3.133333333 + 0.004444444442

Reorder the terms:
0.004444444442 + 0.1333333333x + x2 = 3.133333333 + 0.004444444442

Combine like terms: 3.133333333 + 0.004444444442 = 3.137777777442
0.004444444442 + 0.1333333333x + x2 = 3.137777777442

Factor a perfect square on the left side:
(x + 0.06666666665)(x + 0.06666666665) = 3.137777777442

Calculate the square root of the right side: 1.771377367

Break this problem into two subproblems by setting 
(x + 0.06666666665) equal to 1.771377367 and -1.771377367.

Subproblem 1

x + 0.06666666665 = 1.771377367 Simplifying x + 0.06666666665 = 1.771377367 Reorder the terms: 0.06666666665 + x = 1.771377367 Solving 0.06666666665 + x = 1.771377367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = 1.771377367 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 1.771377367 + -0.06666666665 x = 1.771377367 + -0.06666666665 Combine like terms: 1.771377367 + -0.06666666665 = 1.70471070035 x = 1.70471070035 Simplifying x = 1.70471070035

Subproblem 2

x + 0.06666666665 = -1.771377367 Simplifying x + 0.06666666665 = -1.771377367 Reorder the terms: 0.06666666665 + x = -1.771377367 Solving 0.06666666665 + x = -1.771377367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = -1.771377367 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -1.771377367 + -0.06666666665 x = -1.771377367 + -0.06666666665 Combine like terms: -1.771377367 + -0.06666666665 = -1.83804403365 x = -1.83804403365 Simplifying x = -1.83804403365

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.70471070035, -1.83804403365}

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