(3x^2-5x+6)+(9-8x-4x^2)=

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Solution for (3x^2-5x+6)+(9-8x-4x^2)= equation:


Simplifying
(3x2 + -5x + 6) + (9 + -8x + -4x2) = 0

Reorder the terms:
(6 + -5x + 3x2) + (9 + -8x + -4x2) = 0

Remove parenthesis around (6 + -5x + 3x2)
6 + -5x + 3x2 + (9 + -8x + -4x2) = 0

Remove parenthesis around (9 + -8x + -4x2)
6 + -5x + 3x2 + 9 + -8x + -4x2 = 0

Reorder the terms:
6 + 9 + -5x + -8x + 3x2 + -4x2 = 0

Combine like terms: 6 + 9 = 15
15 + -5x + -8x + 3x2 + -4x2 = 0

Combine like terms: -5x + -8x = -13x
15 + -13x + 3x2 + -4x2 = 0

Combine like terms: 3x2 + -4x2 = -1x2
15 + -13x + -1x2 = 0

Solving
15 + -13x + -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'.
-15 + 13x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 13x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 13x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 13x + x2 = 0 + 15
13x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
13x + x2 = 15

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 15 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 15 + 42.25

Combine like terms: 15 + 42.25 = 57.25
42.25 + 13x + x2 = 57.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(x + 6.5) equal to 7.566372975 and -7.566372975.

Subproblem 1

x + 6.5 = 7.566372975 Simplifying x + 6.5 = 7.566372975 Reorder the terms: 6.5 + x = 7.566372975 Solving 6.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.566372975 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.566372975 + -6.5 x = 7.566372975 + -6.5 Combine like terms: 7.566372975 + -6.5 = 1.066372975 x = 1.066372975 Simplifying x = 1.066372975

Subproblem 2

x + 6.5 = -7.566372975 Simplifying x + 6.5 = -7.566372975 Reorder the terms: 6.5 + x = -7.566372975 Solving 6.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.566372975 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.566372975 + -6.5 x = -7.566372975 + -6.5 Combine like terms: -7.566372975 + -6.5 = -14.066372975 x = -14.066372975 Simplifying x = -14.066372975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.066372975, -14.066372975}

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