3x^2+6x=20

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Solution for 3x^2+6x=20 equation:


Simplifying
3x2 + 6x = 20

Reorder the terms:
6x + 3x2 = 20

Solving
6x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 6x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 6x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 2x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 2x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 2x + x2 = 0 + 6.666666667
2x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
2x + x2 = 6.666666667

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 = 6.666666667 + 1

Reorder the terms:
1 + 2x + x2 = 6.666666667 + 1

Combine like terms: 6.666666667 + 1 = 7.666666667
1 + 2x + x2 = 7.666666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 7.666666667

Calculate the square root of the right side: 2.768874621

Break this problem into two subproblems by setting 
(x + 1) equal to 2.768874621 and -2.768874621.

Subproblem 1

x + 1 = 2.768874621 Simplifying x + 1 = 2.768874621 Reorder the terms: 1 + x = 2.768874621 Solving 1 + x = 2.768874621 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 = 2.768874621 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.768874621 + -1 x = 2.768874621 + -1 Combine like terms: 2.768874621 + -1 = 1.768874621 x = 1.768874621 Simplifying x = 1.768874621

Subproblem 2

x + 1 = -2.768874621 Simplifying x + 1 = -2.768874621 Reorder the terms: 1 + x = -2.768874621 Solving 1 + x = -2.768874621 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 = -2.768874621 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.768874621 + -1 x = -2.768874621 + -1 Combine like terms: -2.768874621 + -1 = -3.768874621 x = -3.768874621 Simplifying x = -3.768874621

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.768874621, -3.768874621}

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