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Simplifying 12x2 + -13x + -13 = 0 Reorder the terms: -13 + -13x + 12x2 = 0 Solving -13 + -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'. -1.083333333 + -1.083333333x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + -1.083333333x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + -1.083333333x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + -1.083333333x + x2 = 0 + 1.083333333 -1.083333333x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 -1.083333333x + x2 = 1.083333333 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 = 1.083333333 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333x + x2 = 1.083333333 + 0.2934027776 Combine like terms: 1.083333333 + 0.2934027776 = 1.3767361106 0.2934027776 + -1.083333333x + x2 = 1.3767361106 Factor a perfect square on the left side: (x + -0.5416666665)(x + -0.5416666665) = 1.3767361106 Calculate the square root of the right side: 1.173343986 Break this problem into two subproblems by setting (x + -0.5416666665) equal to 1.173343986 and -1.173343986.Subproblem 1
x + -0.5416666665 = 1.173343986 Simplifying x + -0.5416666665 = 1.173343986 Reorder the terms: -0.5416666665 + x = 1.173343986 Solving -0.5416666665 + x = 1.173343986 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 = 1.173343986 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = 1.173343986 + 0.5416666665 x = 1.173343986 + 0.5416666665 Combine like terms: 1.173343986 + 0.5416666665 = 1.7150106525 x = 1.7150106525 Simplifying x = 1.7150106525Subproblem 2
x + -0.5416666665 = -1.173343986 Simplifying x + -0.5416666665 = -1.173343986 Reorder the terms: -0.5416666665 + x = -1.173343986 Solving -0.5416666665 + x = -1.173343986 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 = -1.173343986 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = -1.173343986 + 0.5416666665 x = -1.173343986 + 0.5416666665 Combine like terms: -1.173343986 + 0.5416666665 = -0.6316773195 x = -0.6316773195 Simplifying x = -0.6316773195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7150106525, -0.6316773195}
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