(3x^4+9x^3-5)-(7x^2-3x+1)=(3x^4+9x^3-7x+3x-4)

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Solution for (3x^4+9x^3-5)-(7x^2-3x+1)=(3x^4+9x^3-7x+3x-4) equation:


Simplifying
(3x4 + 9x3 + -5) + -1(7x2 + -3x + 1) = (3x4 + 9x3 + -7x + 3x + -4)

Reorder the terms:
(-5 + 9x3 + 3x4) + -1(7x2 + -3x + 1) = (3x4 + 9x3 + -7x + 3x + -4)

Remove parenthesis around (-5 + 9x3 + 3x4)
-5 + 9x3 + 3x4 + -1(7x2 + -3x + 1) = (3x4 + 9x3 + -7x + 3x + -4)

Reorder the terms:
-5 + 9x3 + 3x4 + -1(1 + -3x + 7x2) = (3x4 + 9x3 + -7x + 3x + -4)
-5 + 9x3 + 3x4 + (1 * -1 + -3x * -1 + 7x2 * -1) = (3x4 + 9x3 + -7x + 3x + -4)
-5 + 9x3 + 3x4 + (-1 + 3x + -7x2) = (3x4 + 9x3 + -7x + 3x + -4)

Reorder the terms:
-5 + -1 + 3x + -7x2 + 9x3 + 3x4 = (3x4 + 9x3 + -7x + 3x + -4)

Combine like terms: -5 + -1 = -6
-6 + 3x + -7x2 + 9x3 + 3x4 = (3x4 + 9x3 + -7x + 3x + -4)

Reorder the terms:
-6 + 3x + -7x2 + 9x3 + 3x4 = (-4 + -7x + 3x + 9x3 + 3x4)

Combine like terms: -7x + 3x = -4x
-6 + 3x + -7x2 + 9x3 + 3x4 = (-4 + -4x + 9x3 + 3x4)

Remove parenthesis around (-4 + -4x + 9x3 + 3x4)
-6 + 3x + -7x2 + 9x3 + 3x4 = -4 + -4x + 9x3 + 3x4

Add '-9x3' to each side of the equation.
-6 + 3x + -7x2 + 9x3 + -9x3 + 3x4 = -4 + -4x + 9x3 + -9x3 + 3x4

Combine like terms: 9x3 + -9x3 = 0
-6 + 3x + -7x2 + 0 + 3x4 = -4 + -4x + 9x3 + -9x3 + 3x4
-6 + 3x + -7x2 + 3x4 = -4 + -4x + 9x3 + -9x3 + 3x4

Combine like terms: 9x3 + -9x3 = 0
-6 + 3x + -7x2 + 3x4 = -4 + -4x + 0 + 3x4
-6 + 3x + -7x2 + 3x4 = -4 + -4x + 3x4

Add '-3x4' to each side of the equation.
-6 + 3x + -7x2 + 3x4 + -3x4 = -4 + -4x + 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
-6 + 3x + -7x2 + 0 = -4 + -4x + 3x4 + -3x4
-6 + 3x + -7x2 = -4 + -4x + 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
-6 + 3x + -7x2 = -4 + -4x + 0
-6 + 3x + -7x2 = -4 + -4x

Solving
-6 + 3x + -7x2 = -4 + -4x

Solving for variable 'x'.

Reorder the terms:
-6 + 4 + 3x + 4x + -7x2 = -4 + -4x + 4 + 4x

Combine like terms: -6 + 4 = -2
-2 + 3x + 4x + -7x2 = -4 + -4x + 4 + 4x

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

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

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

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

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.2857142857 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -1x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -1x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + -0.2857142857
-1x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-1x + x2 = -0.2857142857

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.2857142857 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.2857142857 + 0.25

Combine like terms: -0.2857142857 + 0.25 = -0.0357142857
0.25 + -1x + x2 = -0.0357142857

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -0.0357142857

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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