(7x^2+2x)-(3x+8)+(-4x^2-4)=

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Solution for (7x^2+2x)-(3x+8)+(-4x^2-4)= equation:


Simplifying
(7x2 + 2x) + -1(3x + 8) + (-4x2 + -4) = 0

Reorder the terms:
(2x + 7x2) + -1(3x + 8) + (-4x2 + -4) = 0

Remove parenthesis around (2x + 7x2)
2x + 7x2 + -1(3x + 8) + (-4x2 + -4) = 0

Reorder the terms:
2x + 7x2 + -1(8 + 3x) + (-4x2 + -4) = 0
2x + 7x2 + (8 * -1 + 3x * -1) + (-4x2 + -4) = 0
2x + 7x2 + (-8 + -3x) + (-4x2 + -4) = 0

Reorder the terms:
2x + 7x2 + -8 + -3x + (-4 + -4x2) = 0

Remove parenthesis around (-4 + -4x2)
2x + 7x2 + -8 + -3x + -4 + -4x2 = 0

Reorder the terms:
-8 + -4 + 2x + -3x + 7x2 + -4x2 = 0

Combine like terms: -8 + -4 = -12
-12 + 2x + -3x + 7x2 + -4x2 = 0

Combine like terms: 2x + -3x = -1x
-12 + -1x + 7x2 + -4x2 = 0

Combine like terms: 7x2 + -4x2 = 3x2
-12 + -1x + 3x2 = 0

Solving
-12 + -1x + 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'.
-4 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.3333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.3333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.3333333333x + x2 = 0 + 4
-0.3333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.3333333333x + x2 = 4

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 4 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 4 + 0.02777777779

Combine like terms: 4 + 0.02777777779 = 4.02777777779
0.02777777779 + -0.3333333333x + x2 = 4.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 4.02777777779

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 2.00693243 and -2.00693243.

Subproblem 1

x + -0.1666666667 = 2.00693243 Simplifying x + -0.1666666667 = 2.00693243 Reorder the terms: -0.1666666667 + x = 2.00693243 Solving -0.1666666667 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 2.00693243 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 2.00693243 + 0.1666666667 x = 2.00693243 + 0.1666666667 Combine like terms: 2.00693243 + 0.1666666667 = 2.1735990967 x = 2.1735990967 Simplifying x = 2.1735990967

Subproblem 2

x + -0.1666666667 = -2.00693243 Simplifying x + -0.1666666667 = -2.00693243 Reorder the terms: -0.1666666667 + x = -2.00693243 Solving -0.1666666667 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -2.00693243 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -2.00693243 + 0.1666666667 x = -2.00693243 + 0.1666666667 Combine like terms: -2.00693243 + 0.1666666667 = -1.8402657633 x = -1.8402657633 Simplifying x = -1.8402657633

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1735990967, -1.8402657633}

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