(3x^2)-2-8x-10=0

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Solution for (3x^2)-2-8x-10=0 equation:


Simplifying
(3x2) + -2 + -8x + -10 = 0

Reorder the terms:
-2 + -10 + -8x + (3x2) = 0

Combine like terms: -2 + -10 = -12
-12 + -8x + (3x2) = 0

Solving
-12 + -8x + (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'.
-4 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.666666667x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.666666667x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.666666667x + x2 = 0 + 4
-2.666666667x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.666666667x + x2 = 4

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 = 4 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 4 + 1.777777780

Combine like terms: 4 + 1.777777780 = 5.77777778
1.777777780 + -2.666666667x + x2 = 5.77777778

Factor a perfect square on the left side:
((x) + -1.333333334)((x) + -1.333333334) = 5.77777778

Calculate the square root of the right side: 2.403700851

Break this problem into two subproblems by setting 
((x) + -1.333333334) equal to 2.403700851 and -2.403700851.

Subproblem 1

(x) + -1.333333334 = 2.403700851 Simplifying (x) + -1.333333334 = 2.403700851 x + -1.333333334 = 2.403700851 Reorder the terms: -1.333333334 + x = 2.403700851 Solving -1.333333334 + x = 2.403700851 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 = 2.403700851 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.403700851 + 1.333333334 x = 2.403700851 + 1.333333334 Combine like terms: 2.403700851 + 1.333333334 = 3.737034185 x = 3.737034185 Simplifying x = 3.737034185

Subproblem 2

(x) + -1.333333334 = -2.403700851 Simplifying (x) + -1.333333334 = -2.403700851 x + -1.333333334 = -2.403700851 Reorder the terms: -1.333333334 + x = -2.403700851 Solving -1.333333334 + x = -2.403700851 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 = -2.403700851 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.403700851 + 1.333333334 x = -2.403700851 + 1.333333334 Combine like terms: -2.403700851 + 1.333333334 = -1.070367517 x = -1.070367517 Simplifying x = -1.070367517

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.737034185, -1.070367517}

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