x-3*x-3=2x^2-10x+4

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Solution for x-3*x-3=2x^2-10x+4 equation:


Simplifying
x + -3x + -3 = 2x2 + -10x + 4

Reorder the terms:
-3 + x + -3x = 2x2 + -10x + 4

Combine like terms: x + -3x = -2x
-3 + -2x = 2x2 + -10x + 4

Reorder the terms:
-3 + -2x = 4 + -10x + 2x2

Solving
-3 + -2x = 4 + -10x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + -4 + -2x + 10x + -2x2 = 4 + -10x + 2x2 + -4 + 10x + -2x2

Combine like terms: -3 + -4 = -7
-7 + -2x + 10x + -2x2 = 4 + -10x + 2x2 + -4 + 10x + -2x2

Combine like terms: -2x + 10x = 8x
-7 + 8x + -2x2 = 4 + -10x + 2x2 + -4 + 10x + -2x2

Reorder the terms:
-7 + 8x + -2x2 = 4 + -4 + -10x + 10x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-7 + 8x + -2x2 = 0 + -10x + 10x + 2x2 + -2x2
-7 + 8x + -2x2 = -10x + 10x + 2x2 + -2x2

Combine like terms: -10x + 10x = 0
-7 + 8x + -2x2 = 0 + 2x2 + -2x2
-7 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + 8x + -2x2 = 0

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

Divide each side by '-2'.
3.5 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -4x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -4x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -4x + x2 = 0 + -3.5
-4x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-4x + x2 = -3.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -3.5 + 4

Reorder the terms:
4 + -4x + x2 = -3.5 + 4

Combine like terms: -3.5 + 4 = 0.5
4 + -4x + x2 = 0.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + -2) equal to 0.707106781 and -0.707106781.

Subproblem 1

x + -2 = 0.707106781 Simplifying x + -2 = 0.707106781 Reorder the terms: -2 + x = 0.707106781 Solving -2 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.707106781 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.707106781 + 2 x = 0.707106781 + 2 Combine like terms: 0.707106781 + 2 = 2.707106781 x = 2.707106781 Simplifying x = 2.707106781

Subproblem 2

x + -2 = -0.707106781 Simplifying x + -2 = -0.707106781 Reorder the terms: -2 + x = -0.707106781 Solving -2 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.707106781 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.707106781 + 2 x = -0.707106781 + 2 Combine like terms: -0.707106781 + 2 = 1.292893219 x = 1.292893219 Simplifying x = 1.292893219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.707106781, 1.292893219}

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