3x^2+4x=x^2-7x-28

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Solution for 3x^2+4x=x^2-7x-28 equation:


Simplifying
3x2 + 4x = x2 + -7x + -28

Reorder the terms:
4x + 3x2 = x2 + -7x + -28

Reorder the terms:
4x + 3x2 = -28 + -7x + x2

Solving
4x + 3x2 = -28 + -7x + x2

Solving for variable 'x'.

Reorder the terms:
28 + 4x + 7x + 3x2 + -1x2 = -28 + -7x + x2 + 28 + 7x + -1x2

Combine like terms: 4x + 7x = 11x
28 + 11x + 3x2 + -1x2 = -28 + -7x + x2 + 28 + 7x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
28 + 11x + 2x2 = -28 + -7x + x2 + 28 + 7x + -1x2

Reorder the terms:
28 + 11x + 2x2 = -28 + 28 + -7x + 7x + x2 + -1x2

Combine like terms: -28 + 28 = 0
28 + 11x + 2x2 = 0 + -7x + 7x + x2 + -1x2
28 + 11x + 2x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
28 + 11x + 2x2 = 0 + x2 + -1x2
28 + 11x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + 11x + 2x2 = 0

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

Divide each side by '2'.
14 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 5.5x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 5.5x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 5.5x + x2 = 0 + -14
5.5x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
5.5x + x2 = -14

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -14 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -14 + 7.5625

Combine like terms: -14 + 7.5625 = -6.4375
7.5625 + 5.5x + x2 = -6.4375

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = -6.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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