(4x^2-2x+8)-(x^2+3x-2)=0

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Solution for (4x^2-2x+8)-(x^2+3x-2)=0 equation:


Simplifying
(4x2 + -2x + 8) + -1(x2 + 3x + -2) = 0

Reorder the terms:
(8 + -2x + 4x2) + -1(x2 + 3x + -2) = 0

Remove parenthesis around (8 + -2x + 4x2)
8 + -2x + 4x2 + -1(x2 + 3x + -2) = 0

Reorder the terms:
8 + -2x + 4x2 + -1(-2 + 3x + x2) = 0
8 + -2x + 4x2 + (-2 * -1 + 3x * -1 + x2 * -1) = 0
8 + -2x + 4x2 + (2 + -3x + -1x2) = 0

Reorder the terms:
8 + 2 + -2x + -3x + 4x2 + -1x2 = 0

Combine like terms: 8 + 2 = 10
10 + -2x + -3x + 4x2 + -1x2 = 0

Combine like terms: -2x + -3x = -5x
10 + -5x + 4x2 + -1x2 = 0

Combine like terms: 4x2 + -1x2 = 3x2
10 + -5x + 3x2 = 0

Solving
10 + -5x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
3.333333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -1.666666667x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -1.666666667x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + -3.333333333
-1.666666667x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-1.666666667x + x2 = -3.333333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -3.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -3.333333333 + 0.6944444447

Combine like terms: -3.333333333 + 0.6944444447 = -2.6388888883
0.6944444447 + -1.666666667x + x2 = -2.6388888883

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -2.6388888883

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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