3x^2+6x+3=200

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Solution for 3x^2+6x+3=200 equation:


Simplifying
3x2 + 6x + 3 = 200

Reorder the terms:
3 + 6x + 3x2 = 200

Solving
3 + 6x + 3x2 = 200

Solving for variable 'x'.

Reorder the terms:
3 + -200 + 6x + 3x2 = 200 + -200

Combine like terms: 3 + -200 = -197
-197 + 6x + 3x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-197 + 6x + 3x2 = 0

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

Divide each side by '3'.
-65.66666667 + 2x + x2 = 0

Move the constant term to the right:

Add '65.66666667' to each side of the equation.
-65.66666667 + 2x + 65.66666667 + x2 = 0 + 65.66666667

Reorder the terms:
-65.66666667 + 65.66666667 + 2x + x2 = 0 + 65.66666667

Combine like terms: -65.66666667 + 65.66666667 = 0.00000000
0.00000000 + 2x + x2 = 0 + 65.66666667
2x + x2 = 0 + 65.66666667

Combine like terms: 0 + 65.66666667 = 65.66666667
2x + x2 = 65.66666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 65.66666667 + 1

Reorder the terms:
1 + 2x + x2 = 65.66666667 + 1

Combine like terms: 65.66666667 + 1 = 66.66666667
1 + 2x + x2 = 66.66666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 66.66666667

Calculate the square root of the right side: 8.164965809

Break this problem into two subproblems by setting 
(x + 1) equal to 8.164965809 and -8.164965809.

Subproblem 1

x + 1 = 8.164965809 Simplifying x + 1 = 8.164965809 Reorder the terms: 1 + x = 8.164965809 Solving 1 + x = 8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.164965809 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.164965809 + -1 x = 8.164965809 + -1 Combine like terms: 8.164965809 + -1 = 7.164965809 x = 7.164965809 Simplifying x = 7.164965809

Subproblem 2

x + 1 = -8.164965809 Simplifying x + 1 = -8.164965809 Reorder the terms: 1 + x = -8.164965809 Solving 1 + x = -8.164965809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.164965809 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.164965809 + -1 x = -8.164965809 + -1 Combine like terms: -8.164965809 + -1 = -9.164965809 x = -9.164965809 Simplifying x = -9.164965809

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.164965809, -9.164965809}

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