(5x^2+3x+1)+(2x^2+7x)=

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Solution for (5x^2+3x+1)+(2x^2+7x)= equation:


Simplifying
(5x2 + 3x + 1) + (2x2 + 7x) = 0

Reorder the terms:
(1 + 3x + 5x2) + (2x2 + 7x) = 0

Remove parenthesis around (1 + 3x + 5x2)
1 + 3x + 5x2 + (2x2 + 7x) = 0

Reorder the terms:
1 + 3x + 5x2 + (7x + 2x2) = 0

Remove parenthesis around (7x + 2x2)
1 + 3x + 5x2 + 7x + 2x2 = 0

Reorder the terms:
1 + 3x + 7x + 5x2 + 2x2 = 0

Combine like terms: 3x + 7x = 10x
1 + 10x + 5x2 + 2x2 = 0

Combine like terms: 5x2 + 2x2 = 7x2
1 + 10x + 7x2 = 0

Solving
1 + 10x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
0.1428571429 + 1.428571429x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 1.428571429x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 1.428571429x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 1.428571429x + x2 = 0 + -0.1428571429
1.428571429x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
1.428571429x + x2 = -0.1428571429

The x term is 1.428571429x.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429x + 0.5102040819 + x2 = -0.1428571429 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429x + x2 = -0.1428571429 + 0.5102040819

Combine like terms: -0.1428571429 + 0.5102040819 = 0.367346939
0.5102040819 + 1.428571429x + x2 = 0.367346939

Factor a perfect square on the left side:
(x + 0.7142857145)(x + 0.7142857145) = 0.367346939

Calculate the square root of the right side: 0.606091527

Break this problem into two subproblems by setting 
(x + 0.7142857145) equal to 0.606091527 and -0.606091527.

Subproblem 1

x + 0.7142857145 = 0.606091527 Simplifying x + 0.7142857145 = 0.606091527 Reorder the terms: 0.7142857145 + x = 0.606091527 Solving 0.7142857145 + x = 0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 0.606091527 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.606091527 + -0.7142857145 x = 0.606091527 + -0.7142857145 Combine like terms: 0.606091527 + -0.7142857145 = -0.1081941875 x = -0.1081941875 Simplifying x = -0.1081941875

Subproblem 2

x + 0.7142857145 = -0.606091527 Simplifying x + 0.7142857145 = -0.606091527 Reorder the terms: 0.7142857145 + x = -0.606091527 Solving 0.7142857145 + x = -0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -0.606091527 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.606091527 + -0.7142857145 x = -0.606091527 + -0.7142857145 Combine like terms: -0.606091527 + -0.7142857145 = -1.3203772415 x = -1.3203772415 Simplifying x = -1.3203772415

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.1081941875, -1.3203772415}

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