(3x^2+2x-2)-(5x^2-5x+6)=0

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Solution for (3x^2+2x-2)-(5x^2-5x+6)=0 equation:


Simplifying
(3x2 + 2x + -2) + -1(5x2 + -5x + 6) = 0

Reorder the terms:
(-2 + 2x + 3x2) + -1(5x2 + -5x + 6) = 0

Remove parenthesis around (-2 + 2x + 3x2)
-2 + 2x + 3x2 + -1(5x2 + -5x + 6) = 0

Reorder the terms:
-2 + 2x + 3x2 + -1(6 + -5x + 5x2) = 0
-2 + 2x + 3x2 + (6 * -1 + -5x * -1 + 5x2 * -1) = 0
-2 + 2x + 3x2 + (-6 + 5x + -5x2) = 0

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

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

Combine like terms: 2x + 5x = 7x
-8 + 7x + 3x2 + -5x2 = 0

Combine like terms: 3x2 + -5x2 = -2x2
-8 + 7x + -2x2 = 0

Solving
-8 + 7x + -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'.
4 + -3.5x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -4 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -4 + 3.0625

Combine like terms: -4 + 3.0625 = -0.9375
3.0625 + -3.5x + x2 = -0.9375

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = -0.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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