(-6x+6)-(x^2+x-4)=

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Solution for (-6x+6)-(x^2+x-4)= equation:


Simplifying
(-6x + 6) + -1(x2 + x + -4) = 0

Reorder the terms:
(6 + -6x) + -1(x2 + x + -4) = 0

Remove parenthesis around (6 + -6x)
6 + -6x + -1(x2 + x + -4) = 0

Reorder the terms:
6 + -6x + -1(-4 + x + x2) = 0
6 + -6x + (-4 * -1 + x * -1 + x2 * -1) = 0
6 + -6x + (4 + -1x + -1x2) = 0

Reorder the terms:
6 + 4 + -6x + -1x + -1x2 = 0

Combine like terms: 6 + 4 = 10
10 + -6x + -1x + -1x2 = 0

Combine like terms: -6x + -1x = -7x
10 + -7x + -1x2 = 0

Solving
10 + -7x + -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'.
-10 + 7x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 7x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 7x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 7x + x2 = 0 + 10
7x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
7x + x2 = 10

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 10 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + 7x + x2 = 22.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

x + 3.5 = 4.716990566 Simplifying x + 3.5 = 4.716990566 Reorder the terms: 3.5 + x = 4.716990566 Solving 3.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.716990566 + -3.5 x = 4.716990566 + -3.5 Combine like terms: 4.716990566 + -3.5 = 1.216990566 x = 1.216990566 Simplifying x = 1.216990566

Subproblem 2

x + 3.5 = -4.716990566 Simplifying x + 3.5 = -4.716990566 Reorder the terms: 3.5 + x = -4.716990566 Solving 3.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.716990566 + -3.5 x = -4.716990566 + -3.5 Combine like terms: -4.716990566 + -3.5 = -8.216990566 x = -8.216990566 Simplifying x = -8.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.216990566, -8.216990566}

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