-3x^2-7x+1236=960

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Solution for -3x^2-7x+1236=960 equation:


Simplifying
-3x2 + -7x + 1236 = 960

Reorder the terms:
1236 + -7x + -3x2 = 960

Solving
1236 + -7x + -3x2 = 960

Solving for variable 'x'.

Reorder the terms:
1236 + -960 + -7x + -3x2 = 960 + -960

Combine like terms: 1236 + -960 = 276
276 + -7x + -3x2 = 960 + -960

Combine like terms: 960 + -960 = 0
276 + -7x + -3x2 = 0

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

Divide each side by '-3'.
-92 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '92' to each side of the equation.
-92 + 2.333333333x + 92 + x2 = 0 + 92

Reorder the terms:
-92 + 92 + 2.333333333x + x2 = 0 + 92

Combine like terms: -92 + 92 = 0
0 + 2.333333333x + x2 = 0 + 92
2.333333333x + x2 = 0 + 92

Combine like terms: 0 + 92 = 92
2.333333333x + x2 = 92

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 = 92 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 92 + 1.361111112

Combine like terms: 92 + 1.361111112 = 93.361111112
1.361111112 + 2.333333333x + x2 = 93.361111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 93.361111112

Calculate the square root of the right side: 9.66235536

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 9.66235536 and -9.66235536.


Subproblem 1
x + 1.166666667 = 9.66235536

Simplifying
x + 1.166666667 = 9.66235536

Reorder the terms:
1.166666667 + x = 9.66235536

Solving
1.166666667 + x = 9.66235536

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 = 9.66235536 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 9.66235536 + -1.166666667
x = 9.66235536 + -1.166666667

Combine like terms: 9.66235536 + -1.166666667 = 8.495688693
x = 8.495688693

Simplifying
x = 8.495688693


Subproblem 2
x + 1.166666667 = -9.66235536

Simplifying
x + 1.166666667 = -9.66235536

Reorder the terms:
1.166666667 + x = -9.66235536

Solving
1.166666667 + x = -9.66235536

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 = -9.66235536 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -9.66235536 + -1.166666667
x = -9.66235536 + -1.166666667

Combine like terms: -9.66235536 + -1.166666667 = -10.829022027
x = -10.829022027

Simplifying
x = -10.829022027


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.495688693, -10.829022027}

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