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Simplifying 0 = 3x2 + -12x + -4 Reorder the terms: 0 = -4 + -12x + 3x2 Solving 0 = -4 + -12x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + 12x + -3x2 = -4 + -12x + 3x2 + 4 + 12x + -3x2 Reorder the terms: 4 + 12x + -3x2 = -4 + 4 + -12x + 12x + 3x2 + -3x2 Combine like terms: -4 + 4 = 0 4 + 12x + -3x2 = 0 + -12x + 12x + 3x2 + -3x2 4 + 12x + -3x2 = -12x + 12x + 3x2 + -3x2 Combine like terms: -12x + 12x = 0 4 + 12x + -3x2 = 0 + 3x2 + -3x2 4 + 12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 4 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + -4x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -4x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -4x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -4x + x2 = 0 + 1.333333333 -4x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -4x + x2 = 1.333333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 1.333333333 + 4 Reorder the terms: 4 + -4x + x2 = 1.333333333 + 4 Combine like terms: 1.333333333 + 4 = 5.333333333 4 + -4x + x2 = 5.333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (x + -2) equal to 2.309401077 and -2.309401077.Subproblem 1
x + -2 = 2.309401077 Simplifying x + -2 = 2.309401077 Reorder the terms: -2 + x = 2.309401077 Solving -2 + x = 2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.309401077 + 2 x = 2.309401077 + 2 Combine like terms: 2.309401077 + 2 = 4.309401077 x = 4.309401077 Simplifying x = 4.309401077Subproblem 2
x + -2 = -2.309401077 Simplifying x + -2 = -2.309401077 Reorder the terms: -2 + x = -2.309401077 Solving -2 + x = -2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.309401077 + 2 x = -2.309401077 + 2 Combine like terms: -2.309401077 + 2 = -0.309401077 x = -0.309401077 Simplifying x = -0.309401077Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.309401077, -0.309401077}
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