0=2x^2+12x-4

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Solution for 0=2x^2+12x-4 equation:


Simplifying
0 = 2x2 + 12x + -4

Reorder the terms:
0 = -4 + 12x + 2x2

Solving
0 = -4 + 12x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + -12x + -2x2 = -4 + 12x + 2x2 + 4 + -12x + -2x2

Reorder the terms:
4 + -12x + -2x2 = -4 + 4 + 12x + -12x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
4 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2
4 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
4 + -12x + -2x2 = 0 + 2x2 + -2x2
4 + -12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + -12x + -2x2 = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -6x + -1x2 = 0 Solving 2 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 6x + x2 = 0 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}

Solution

x = {0.31662479, -6.31662479}

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