3x^2-7x-56=0

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Solution for 3x^2-7x-56=0 equation: 


Simplifying
3x2 + -7x + -56 = 0

Reorder the terms:
-56 + -7x + 3x2 = 0

Solving
-56 + -7x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-18.66666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '18.66666667' to each side of the equation.
-18.66666667 + -2.333333333x + 18.66666667 + x2 = 0 + 18.66666667

Reorder the terms:
-18.66666667 + 18.66666667 + -2.333333333x + x2 = 0 + 18.66666667

Combine like terms: -18.66666667 + 18.66666667 = 0.00000000
0.00000000 + -2.333333333x + x2 = 0 + 18.66666667
-2.333333333x + x2 = 0 + 18.66666667

Combine like terms: 0 + 18.66666667 = 18.66666667
-2.333333333x + x2 = 18.66666667

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 = 18.66666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 18.66666667 + 1.361111112

Combine like terms: 18.66666667 + 1.361111112 = 20.027777782
1.361111112 + -2.333333333x + x2 = 20.027777782

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 20.027777782

Calculate the square root of the right side: 4.475240528

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 4.475240528 and -4.475240528.


Subproblem 1
x + -1.166666667 = 4.475240528

Simplifying
x + -1.166666667 = 4.475240528

Reorder the terms:
-1.166666667 + x = 4.475240528

Solving
-1.166666667 + x = 4.475240528

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 = 4.475240528 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 4.475240528 + 1.166666667
x = 4.475240528 + 1.166666667

Combine like terms: 4.475240528 + 1.166666667 = 5.641907195
x = 5.641907195

Simplifying
x = 5.641907195


Subproblem 2
x + -1.166666667 = -4.475240528

Simplifying
x + -1.166666667 = -4.475240528

Reorder the terms:
-1.166666667 + x = -4.475240528

Solving
-1.166666667 + x = -4.475240528

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 = -4.475240528 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -4.475240528 + 1.166666667
x = -4.475240528 + 1.166666667

Combine like terms: -4.475240528 + 1.166666667 = -3.308573861
x = -3.308573861

Simplifying
x = -3.308573861


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.641907195, -3.308573861}

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