6x^2-31x+43=-7x+8

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Solution for 6x^2-31x+43=-7x+8 equation: 


Simplifying
6x2 + -31x + 43 = -7x + 8

Reorder the terms:
43 + -31x + 6x2 = -7x + 8

Reorder the terms:
43 + -31x + 6x2 = 8 + -7x

Solving
43 + -31x + 6x2 = 8 + -7x

Solving for variable 'x'.

Reorder the terms:
43 + -8 + -31x + 7x + 6x2 = 8 + -7x + -8 + 7x

Combine like terms: 43 + -8 = 35
35 + -31x + 7x + 6x2 = 8 + -7x + -8 + 7x

Combine like terms: -31x + 7x = -24x
35 + -24x + 6x2 = 8 + -7x + -8 + 7x

Reorder the terms:
35 + -24x + 6x2 = 8 + -8 + -7x + 7x

Combine like terms: 8 + -8 = 0
35 + -24x + 6x2 = 0 + -7x + 7x
35 + -24x + 6x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
35 + -24x + 6x2 = 0

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

Divide each side by '6'.
5.833333333 + -4x + x2 = 0

Move the constant term to the right:

Add '-5.833333333' to each side of the equation.
5.833333333 + -4x + -5.833333333 + x2 = 0 + -5.833333333

Reorder the terms:
5.833333333 + -5.833333333 + -4x + x2 = 0 + -5.833333333

Combine like terms: 5.833333333 + -5.833333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + -5.833333333
-4x + x2 = 0 + -5.833333333

Combine like terms: 0 + -5.833333333 = -5.833333333
-4x + x2 = -5.833333333

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 = -5.833333333 + 4

Reorder the terms:
4 + -4x + x2 = -5.833333333 + 4

Combine like terms: -5.833333333 + 4 = -1.833333333
4 + -4x + x2 = -1.833333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = -1.833333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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