960-8x=3x^2

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Solution for 960-8x=3x^2 equation:


Simplifying
960 + -8x = 3x2

Solving
960 + -8x = 3x2

Solving for variable 'x'.

Combine like terms: 3x2 + -3x2 = 0
960 + -8x + -3x2 = 0

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

Divide each side by '-3'.
-320 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + 2.666666667x + 320 + x2 = 0 + 320

Reorder the terms:
-320 + 320 + 2.666666667x + x2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 2.666666667x + x2 = 0 + 320
2.666666667x + x2 = 0 + 320

Combine like terms: 0 + 320 = 320
2.666666667x + x2 = 320

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 320 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 320 + 1.777777780

Combine like terms: 320 + 1.777777780 = 321.77777778
1.777777780 + 2.666666667x + x2 = 321.77777778

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 321.77777778

Calculate the square root of the right side: 17.938165396

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 17.938165396 and -17.938165396.

Subproblem 1

x + 1.333333334 = 17.938165396 Simplifying x + 1.333333334 = 17.938165396 Reorder the terms: 1.333333334 + x = 17.938165396 Solving 1.333333334 + x = 17.938165396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 17.938165396 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 17.938165396 + -1.333333334 x = 17.938165396 + -1.333333334 Combine like terms: 17.938165396 + -1.333333334 = 16.604832062 x = 16.604832062 Simplifying x = 16.604832062

Subproblem 2

x + 1.333333334 = -17.938165396 Simplifying x + 1.333333334 = -17.938165396 Reorder the terms: 1.333333334 + x = -17.938165396 Solving 1.333333334 + x = -17.938165396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -17.938165396 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -17.938165396 + -1.333333334 x = -17.938165396 + -1.333333334 Combine like terms: -17.938165396 + -1.333333334 = -19.27149873 x = -19.27149873 Simplifying x = -19.27149873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.604832062, -19.27149873}

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