(x*x)+6x=2

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Solution for (x*x)+6x=2 equation:


Simplifying
(x * x) + 6x = 2

Multiply x * x
(x2) + 6x = 2
x2 + 6x = 2

Reorder the terms:
6x + x2 = 2

Solving
6x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 6x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 6x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6x + x2 = 0 + 2
6x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
6x + x2 = 2

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 = 2 + 9

Reorder the terms:
9 + 6x + x2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + 6x + x2 = 11

Factor a perfect square on the left side:
(x + 3)(x + 3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 3) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + 3 = 3.31662479 Simplifying x + 3 = 3.31662479 Reorder the terms: 3 + x = 3.31662479 Solving 3 + x = 3.31662479 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 = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.31662479 + -3 x = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 x = 0.31662479 Simplifying x = 0.31662479

Subproblem 2

x + 3 = -3.31662479 Simplifying x + 3 = -3.31662479 Reorder the terms: 3 + x = -3.31662479 Solving 3 + x = -3.31662479 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 = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.31662479 + -3 x = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 x = -6.31662479 Simplifying x = -6.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.31662479, -6.31662479}

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