3x^2-7x=47

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Solution for 3x^2-7x=47 equation: 


Simplifying
3x2 + -7x = 47

Reorder the terms:
-7x + 3x2 = 47

Solving
-7x + 3x2 = 47

Solving for variable 'x'.

Reorder the terms:
-47 + -7x + 3x2 = 47 + -47

Combine like terms: 47 + -47 = 0
-47 + -7x + 3x2 = 0

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

Divide each side by '3'.
-15.66666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '15.66666667' to each side of the equation.
-15.66666667 + -2.333333333x + 15.66666667 + x2 = 0 + 15.66666667

Reorder the terms:
-15.66666667 + 15.66666667 + -2.333333333x + x2 = 0 + 15.66666667

Combine like terms: -15.66666667 + 15.66666667 = 0.00000000
0.00000000 + -2.333333333x + x2 = 0 + 15.66666667
-2.333333333x + x2 = 0 + 15.66666667

Combine like terms: 0 + 15.66666667 = 15.66666667
-2.333333333x + x2 = 15.66666667

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 = 15.66666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 15.66666667 + 1.361111112

Combine like terms: 15.66666667 + 1.361111112 = 17.027777782
1.361111112 + -2.333333333x + x2 = 17.027777782

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 17.027777782

Calculate the square root of the right side: 4.126472802

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 4.126472802 and -4.126472802.


Subproblem 1
x + -1.166666667 = 4.126472802

Simplifying
x + -1.166666667 = 4.126472802

Reorder the terms:
-1.166666667 + x = 4.126472802

Solving
-1.166666667 + x = 4.126472802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 4.126472802 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 4.126472802 + 1.166666667
x = 4.126472802 + 1.166666667

Combine like terms: 4.126472802 + 1.166666667 = 5.293139469
x = 5.293139469

Simplifying
x = 5.293139469


Subproblem 2
x + -1.166666667 = -4.126472802

Simplifying
x + -1.166666667 = -4.126472802

Reorder the terms:
-1.166666667 + x = -4.126472802

Solving
-1.166666667 + x = -4.126472802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -4.126472802 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -4.126472802 + 1.166666667
x = -4.126472802 + 1.166666667

Combine like terms: -4.126472802 + 1.166666667 = -2.959806135
x = -2.959806135

Simplifying
x = -2.959806135


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.293139469, -2.959806135}

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