7x+3=x(3x+1)-x+8

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Solution for 7x+3=x(3x+1)-x+8 equation: 


Simplifying
7x + 3 = x(3x + 1) + -1x + 8

Reorder the terms:
3 + 7x = x(3x + 1) + -1x + 8

Reorder the terms:
3 + 7x = x(1 + 3x) + -1x + 8
3 + 7x = (1 * x + 3x * x) + -1x + 8
3 + 7x = (1x + 3x2) + -1x + 8

Reorder the terms:
3 + 7x = 8 + 1x + -1x + 3x2

Combine like terms: 1x + -1x = 0
3 + 7x = 8 + 0 + 3x2
3 + 7x = 8 + 3x2

Solving
3 + 7x = 8 + 3x2

Solving for variable 'x'.

Reorder the terms:
3 + -8 + 7x + -3x2 = 8 + 3x2 + -8 + -3x2

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

Reorder the terms:
-5 + 7x + -3x2 = 8 + -8 + 3x2 + -3x2

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

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

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

Divide each side by '-3'.
1.666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -2.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -2.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + -1.666666667
-2.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-2.333333333x + x2 = -1.666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -1.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -1.666666667 + 1.361111112

Combine like terms: -1.666666667 + 1.361111112 = -0.305555555
1.361111112 + -2.333333333x + x2 = -0.305555555

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = -0.305555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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