(2x^2-4x+8)-(3x^2+10x+2)=

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Solution for (2x^2-4x+8)-(3x^2+10x+2)= equation:


Simplifying
(2x2 + -4x + 8) + -1(3x2 + 10x + 2) = 0

Reorder the terms:
(8 + -4x + 2x2) + -1(3x2 + 10x + 2) = 0

Remove parenthesis around (8 + -4x + 2x2)
8 + -4x + 2x2 + -1(3x2 + 10x + 2) = 0

Reorder the terms:
8 + -4x + 2x2 + -1(2 + 10x + 3x2) = 0
8 + -4x + 2x2 + (2 * -1 + 10x * -1 + 3x2 * -1) = 0
8 + -4x + 2x2 + (-2 + -10x + -3x2) = 0

Reorder the terms:
8 + -2 + -4x + -10x + 2x2 + -3x2 = 0

Combine like terms: 8 + -2 = 6
6 + -4x + -10x + 2x2 + -3x2 = 0

Combine like terms: -4x + -10x = -14x
6 + -14x + 2x2 + -3x2 = 0

Combine like terms: 2x2 + -3x2 = -1x2
6 + -14x + -1x2 = 0

Solving
6 + -14x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 14x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 14x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 14x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 14x + x2 = 0 + 6
14x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
14x + x2 = 6

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 6 + 49

Reorder the terms:
49 + 14x + x2 = 6 + 49

Combine like terms: 6 + 49 = 55
49 + 14x + x2 = 55

Factor a perfect square on the left side:
(x + 7)(x + 7) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 7) equal to 7.416198487 and -7.416198487.

Subproblem 1

x + 7 = 7.416198487 Simplifying x + 7 = 7.416198487 Reorder the terms: 7 + x = 7.416198487 Solving 7 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.416198487 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.416198487 + -7 x = 7.416198487 + -7 Combine like terms: 7.416198487 + -7 = 0.416198487 x = 0.416198487 Simplifying x = 0.416198487

Subproblem 2

x + 7 = -7.416198487 Simplifying x + 7 = -7.416198487 Reorder the terms: 7 + x = -7.416198487 Solving 7 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.416198487 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.416198487 + -7 x = -7.416198487 + -7 Combine like terms: -7.416198487 + -7 = -14.416198487 x = -14.416198487 Simplifying x = -14.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.416198487, -14.416198487}

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