-3x^2-18x+10=0

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Solution for -3x^2-18x+10=0 equation:


Simplifying
-3x2 + -18x + 10 = 0

Reorder the terms:
10 + -18x + -3x2 = 0

Solving
10 + -18x + -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'.
-3.333333333 + 6x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 6x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 6x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 6x + x2 = 0 + 3.333333333
6x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
6x + x2 = 3.333333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 3.333333333 + 9

Reorder the terms:
9 + 6x + x2 = 3.333333333 + 9

Combine like terms: 3.333333333 + 9 = 12.333333333
9 + 6x + x2 = 12.333333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 12.333333333

Calculate the square root of the right side: 3.511884584

Break this problem into two subproblems by setting 
(x + 3) equal to 3.511884584 and -3.511884584.

Subproblem 1

x + 3 = 3.511884584 Simplifying x + 3 = 3.511884584 Reorder the terms: 3 + x = 3.511884584 Solving 3 + x = 3.511884584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.511884584 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.511884584 + -3 x = 3.511884584 + -3 Combine like terms: 3.511884584 + -3 = 0.511884584 x = 0.511884584 Simplifying x = 0.511884584

Subproblem 2

x + 3 = -3.511884584 Simplifying x + 3 = -3.511884584 Reorder the terms: 3 + x = -3.511884584 Solving 3 + x = -3.511884584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.511884584 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.511884584 + -3 x = -3.511884584 + -3 Combine like terms: -3.511884584 + -3 = -6.511884584 x = -6.511884584 Simplifying x = -6.511884584

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.511884584, -6.511884584}

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