-6x^2+8-5+3x+2x-4x^2=

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


Simplifying
-6x2 + 8 + -5 + 3x + 2x + -4x2 = 0

Reorder the terms:
8 + -5 + 3x + 2x + -6x2 + -4x2 = 0

Combine like terms: 8 + -5 = 3
3 + 3x + 2x + -6x2 + -4x2 = 0

Combine like terms: 3x + 2x = 5x
3 + 5x + -6x2 + -4x2 = 0

Combine like terms: -6x2 + -4x2 = -10x2
3 + 5x + -10x2 = 0

Solving
3 + 5x + -10x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.3 + -0.5x + x2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + -0.5x + 0.3 + x2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + -0.5x + x2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + -0.5x + x2 = 0.0 + 0.3
-0.5x + x2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
-0.5x + x2 = 0.3

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.3 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.3 + 0.0625

Combine like terms: 0.3 + 0.0625 = 0.3625
0.0625 + -0.5x + x2 = 0.3625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.3625

Calculate the square root of the right side: 0.602079729

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.602079729 and -0.602079729.

Subproblem 1

x + -0.25 = 0.602079729 Simplifying x + -0.25 = 0.602079729 Reorder the terms: -0.25 + x = 0.602079729 Solving -0.25 + x = 0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.602079729 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.602079729 + 0.25 x = 0.602079729 + 0.25 Combine like terms: 0.602079729 + 0.25 = 0.852079729 x = 0.852079729 Simplifying x = 0.852079729

Subproblem 2

x + -0.25 = -0.602079729 Simplifying x + -0.25 = -0.602079729 Reorder the terms: -0.25 + x = -0.602079729 Solving -0.25 + x = -0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.602079729 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.602079729 + 0.25 x = -0.602079729 + 0.25 Combine like terms: -0.602079729 + 0.25 = -0.352079729 x = -0.352079729 Simplifying x = -0.352079729

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.852079729, -0.352079729}

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