2x^2+6x=2-6x

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Solution for 2x^2+6x=2-6x equation:


Simplifying
2x2 + 6x = 2 + -6x

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

Solving
6x + 2x2 = 2 + -6x

Solving for variable 'x'.

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

Combine like terms: 6x + 6x = 12x
-2 + 12x + 2x2 = 2 + -6x + -2 + 6x

Reorder the terms:
-2 + 12x + 2x2 = 2 + -2 + -6x + 6x

Combine like terms: 2 + -2 = 0
-2 + 12x + 2x2 = 0 + -6x + 6x
-2 + 12x + 2x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-2 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 6x + x2)' equal to zero and attempt to solve: Simplifying -1 + 6x + x2 = 0 Solving -1 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6x + x2 = 0 + 1 6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 6x + x2 = 1 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 = 1 + 9 Reorder the terms: 9 + 6x + x2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6x + x2 = 10 Factor a perfect square on the left side: (x + 3)(x + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + 3 = 3.16227766 Simplifying x + 3 = 3.16227766 Reorder the terms: 3 + x = 3.16227766 Solving 3 + x = 3.16227766 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 = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.16227766 + -3 x = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 x = 0.16227766 Simplifying x = 0.16227766

Subproblem 2

x + 3 = -3.16227766 Simplifying x + 3 = -3.16227766 Reorder the terms: 3 + x = -3.16227766 Solving 3 + x = -3.16227766 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 = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.16227766 + -3 x = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 x = -6.16227766 Simplifying x = -6.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.16227766, -6.16227766}

Solution

x = {0.16227766, -6.16227766}

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