(3x^2-4x+8)-(x^2+7x-5)=

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Solution for (3x^2-4x+8)-(x^2+7x-5)= equation:


Simplifying
(3x2 + -4x + 8) + -1(x2 + 7x + -5) = 0

Reorder the terms:
(8 + -4x + 3x2) + -1(x2 + 7x + -5) = 0

Remove parenthesis around (8 + -4x + 3x2)
8 + -4x + 3x2 + -1(x2 + 7x + -5) = 0

Reorder the terms:
8 + -4x + 3x2 + -1(-5 + 7x + x2) = 0
8 + -4x + 3x2 + (-5 * -1 + 7x * -1 + x2 * -1) = 0
8 + -4x + 3x2 + (5 + -7x + -1x2) = 0

Reorder the terms:
8 + 5 + -4x + -7x + 3x2 + -1x2 = 0

Combine like terms: 8 + 5 = 13
13 + -4x + -7x + 3x2 + -1x2 = 0

Combine like terms: -4x + -7x = -11x
13 + -11x + 3x2 + -1x2 = 0

Combine like terms: 3x2 + -1x2 = 2x2
13 + -11x + 2x2 = 0

Solving
13 + -11x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
6.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -5.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -5.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -5.5x + x2 = 0 + -6.5
-5.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-5.5x + x2 = -6.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -6.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -6.5 + 7.5625

Combine like terms: -6.5 + 7.5625 = 1.0625
7.5625 + -5.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + -2.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + -2.75 = 1.030776406 Simplifying x + -2.75 = 1.030776406 Reorder the terms: -2.75 + x = 1.030776406 Solving -2.75 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 1.030776406 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 1.030776406 + 2.75 x = 1.030776406 + 2.75 Combine like terms: 1.030776406 + 2.75 = 3.780776406 x = 3.780776406 Simplifying x = 3.780776406

Subproblem 2

x + -2.75 = -1.030776406 Simplifying x + -2.75 = -1.030776406 Reorder the terms: -2.75 + x = -1.030776406 Solving -2.75 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -1.030776406 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -1.030776406 + 2.75 x = -1.030776406 + 2.75 Combine like terms: -1.030776406 + 2.75 = 1.719223594 x = 1.719223594 Simplifying x = 1.719223594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.780776406, 1.719223594}

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