(7x^2-6x-49)+(8x^2+8x)=

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Solution for (7x^2-6x-49)+(8x^2+8x)= equation:


Simplifying
(7x2 + -6x + -49) + (8x2 + 8x) = 0

Reorder the terms:
(-49 + -6x + 7x2) + (8x2 + 8x) = 0

Remove parenthesis around (-49 + -6x + 7x2)
-49 + -6x + 7x2 + (8x2 + 8x) = 0

Reorder the terms:
-49 + -6x + 7x2 + (8x + 8x2) = 0

Remove parenthesis around (8x + 8x2)
-49 + -6x + 7x2 + 8x + 8x2 = 0

Reorder the terms:
-49 + -6x + 8x + 7x2 + 8x2 = 0

Combine like terms: -6x + 8x = 2x
-49 + 2x + 7x2 + 8x2 = 0

Combine like terms: 7x2 + 8x2 = 15x2
-49 + 2x + 15x2 = 0

Solving
-49 + 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'.
-3.266666667 + 0.1333333333x + x2 = 0

Move the constant term to the right:

Add '3.266666667' to each side of the equation.
-3.266666667 + 0.1333333333x + 3.266666667 + x2 = 0 + 3.266666667

Reorder the terms:
-3.266666667 + 3.266666667 + 0.1333333333x + x2 = 0 + 3.266666667

Combine like terms: -3.266666667 + 3.266666667 = 0.000000000
0.000000000 + 0.1333333333x + x2 = 0 + 3.266666667
0.1333333333x + x2 = 0 + 3.266666667

Combine like terms: 0 + 3.266666667 = 3.266666667
0.1333333333x + x2 = 3.266666667

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 = 3.266666667 + 0.004444444442

Reorder the terms:
0.004444444442 + 0.1333333333x + x2 = 3.266666667 + 0.004444444442

Combine like terms: 3.266666667 + 0.004444444442 = 3.271111111442
0.004444444442 + 0.1333333333x + x2 = 3.271111111442

Factor a perfect square on the left side:
(x + 0.06666666665)(x + 0.06666666665) = 3.271111111442

Calculate the square root of the right side: 1.808621329

Break this problem into two subproblems by setting 
(x + 0.06666666665) equal to 1.808621329 and -1.808621329.

Subproblem 1

x + 0.06666666665 = 1.808621329 Simplifying x + 0.06666666665 = 1.808621329 Reorder the terms: 0.06666666665 + x = 1.808621329 Solving 0.06666666665 + x = 1.808621329 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 = 1.808621329 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 1.808621329 + -0.06666666665 x = 1.808621329 + -0.06666666665 Combine like terms: 1.808621329 + -0.06666666665 = 1.74195466235 x = 1.74195466235 Simplifying x = 1.74195466235

Subproblem 2

x + 0.06666666665 = -1.808621329 Simplifying x + 0.06666666665 = -1.808621329 Reorder the terms: 0.06666666665 + x = -1.808621329 Solving 0.06666666665 + x = -1.808621329 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 = -1.808621329 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -1.808621329 + -0.06666666665 x = -1.808621329 + -0.06666666665 Combine like terms: -1.808621329 + -0.06666666665 = -1.87528799565 x = -1.87528799565 Simplifying x = -1.87528799565

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.74195466235, -1.87528799565}

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