3x^2-5x-4-7x+5-x^2=

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


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

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

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

Combine like terms: -5x + -7x = -12x
1 + -12x + 3x2 + -1x2 = 0

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

Solving
1 + -12x + 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'.
0.5 + -6x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -6x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -6x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -6x + x2 = 0 + -0.5
-6x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-6x + x2 = -0.5

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -0.5 + 9

Reorder the terms:
9 + -6x + x2 = -0.5 + 9

Combine like terms: -0.5 + 9 = 8.5
9 + -6x + x2 = 8.5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + -3) equal to 2.915475947 and -2.915475947.


Subproblem 1
x + -3 = 2.915475947

Simplifying
x + -3 = 2.915475947

Reorder the terms:
-3 + x = 2.915475947

Solving
-3 + x = 2.915475947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = 2.915475947 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.915475947 + 3
x = 2.915475947 + 3

Combine like terms: 2.915475947 + 3 = 5.915475947
x = 5.915475947

Simplifying
x = 5.915475947


Subproblem 2
x + -3 = -2.915475947

Simplifying
x + -3 = -2.915475947

Reorder the terms:
-3 + x = -2.915475947

Solving
-3 + x = -2.915475947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = -2.915475947 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.915475947 + 3
x = -2.915475947 + 3

Combine like terms: -2.915475947 + 3 = 0.084524053
x = 0.084524053

Simplifying
x = 0.084524053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.915475947, 0.084524053}

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