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Simplifying -12x2 + -13x + 3 = 0 Reorder the terms: 3 + -13x + -12x2 = 0 Solving 3 + -13x + -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 + 1.083333333x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.083333333x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.083333333x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.083333333x + x2 = 0 + 0.25 1.083333333x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 1.083333333x + x2 = 0.25 The x term is 1.083333333x. Take half its coefficient (0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. 1.083333333x + 0.2934027776 + x2 = 0.25 + 0.2934027776 Reorder the terms: 0.2934027776 + 1.083333333x + x2 = 0.25 + 0.2934027776 Combine like terms: 0.25 + 0.2934027776 = 0.5434027776 0.2934027776 + 1.083333333x + x2 = 0.5434027776 Factor a perfect square on the left side: (x + 0.5416666665)(x + 0.5416666665) = 0.5434027776 Calculate the square root of the right side: 0.737158584 Break this problem into two subproblems by setting (x + 0.5416666665) equal to 0.737158584 and -0.737158584.Subproblem 1
x + 0.5416666665 = 0.737158584 Simplifying x + 0.5416666665 = 0.737158584 Reorder the terms: 0.5416666665 + x = 0.737158584 Solving 0.5416666665 + x = 0.737158584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = 0.737158584 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = 0.737158584 + -0.5416666665 x = 0.737158584 + -0.5416666665 Combine like terms: 0.737158584 + -0.5416666665 = 0.1954919175 x = 0.1954919175 Simplifying x = 0.1954919175Subproblem 2
x + 0.5416666665 = -0.737158584 Simplifying x + 0.5416666665 = -0.737158584 Reorder the terms: 0.5416666665 + x = -0.737158584 Solving 0.5416666665 + x = -0.737158584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = -0.737158584 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = -0.737158584 + -0.5416666665 x = -0.737158584 + -0.5416666665 Combine like terms: -0.737158584 + -0.5416666665 = -1.2788252505 x = -1.2788252505 Simplifying x = -1.2788252505Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1954919175, -1.2788252505}
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