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Simplifying 0 = 12x2 + 3x + -2 Reorder the terms: 0 = -2 + 3x + 12x2 Solving 0 = -2 + 3x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + -3x + -12x2 = -2 + 3x + 12x2 + 2 + -3x + -12x2 Reorder the terms: 2 + -3x + -12x2 = -2 + 2 + 3x + -3x + 12x2 + -12x2 Combine like terms: -2 + 2 = 0 2 + -3x + -12x2 = 0 + 3x + -3x + 12x2 + -12x2 2 + -3x + -12x2 = 3x + -3x + 12x2 + -12x2 Combine like terms: 3x + -3x = 0 2 + -3x + -12x2 = 0 + 12x2 + -12x2 2 + -3x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 2 + -3x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.1666666667 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.25x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.25x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.25x + x2 = 0 + 0.1666666667 0.25x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.25x + x2 = 0.1666666667 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.1666666667 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.1666666667 + 0.015625 Combine like terms: 0.1666666667 + 0.015625 = 0.1822916667 0.015625 + 0.25x + x2 = 0.1822916667 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.1822916667 Calculate the square root of the right side: 0.426956282 Break this problem into two subproblems by setting (x + 0.125) equal to 0.426956282 and -0.426956282.Subproblem 1
x + 0.125 = 0.426956282 Simplifying x + 0.125 = 0.426956282 Reorder the terms: 0.125 + x = 0.426956282 Solving 0.125 + x = 0.426956282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.426956282 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.426956282 + -0.125 x = 0.426956282 + -0.125 Combine like terms: 0.426956282 + -0.125 = 0.301956282 x = 0.301956282 Simplifying x = 0.301956282Subproblem 2
x + 0.125 = -0.426956282 Simplifying x + 0.125 = -0.426956282 Reorder the terms: 0.125 + x = -0.426956282 Solving 0.125 + x = -0.426956282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.426956282 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.426956282 + -0.125 x = -0.426956282 + -0.125 Combine like terms: -0.426956282 + -0.125 = -0.551956282 x = -0.551956282 Simplifying x = -0.551956282Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.301956282, -0.551956282}
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