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Simplifying 12x2 + -16x + 3 = 0 Reorder the terms: 3 + -16x + 12x2 = 0 Solving 3 + -16x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.25 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.333333333x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.333333333x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.333333333x + x2 = 0 + -0.25 -1.333333333x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.333333333x + x2 = -0.25 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -0.25 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.25 + 0.4444444442 Combine like terms: -0.25 + 0.4444444442 = 0.1944444442 0.4444444442 + -1.333333333x + x2 = 0.1944444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.1944444442 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.440958552 and -0.440958552.Subproblem 1
x + -0.6666666665 = 0.440958552 Simplifying x + -0.6666666665 = 0.440958552 Reorder the terms: -0.6666666665 + x = 0.440958552 Solving -0.6666666665 + x = 0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 0.440958552 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.440958552 + 0.6666666665 x = 0.440958552 + 0.6666666665 Combine like terms: 0.440958552 + 0.6666666665 = 1.1076252185 x = 1.1076252185 Simplifying x = 1.1076252185Subproblem 2
x + -0.6666666665 = -0.440958552 Simplifying x + -0.6666666665 = -0.440958552 Reorder the terms: -0.6666666665 + x = -0.440958552 Solving -0.6666666665 + x = -0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -0.440958552 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.440958552 + 0.6666666665 x = -0.440958552 + 0.6666666665 Combine like terms: -0.440958552 + 0.6666666665 = 0.2257081145 x = 0.2257081145 Simplifying x = 0.2257081145Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1076252185, 0.2257081145}
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