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Simplifying (19x2 + 12x + -12) + -1(7x2 + -10x + 13) = 0 Reorder the terms: (-12 + 12x + 19x2) + -1(7x2 + -10x + 13) = 0 Remove parenthesis around (-12 + 12x + 19x2) -12 + 12x + 19x2 + -1(7x2 + -10x + 13) = 0 Reorder the terms: -12 + 12x + 19x2 + -1(13 + -10x + 7x2) = 0 -12 + 12x + 19x2 + (13 * -1 + -10x * -1 + 7x2 * -1) = 0 -12 + 12x + 19x2 + (-13 + 10x + -7x2) = 0 Reorder the terms: -12 + -13 + 12x + 10x + 19x2 + -7x2 = 0 Combine like terms: -12 + -13 = -25 -25 + 12x + 10x + 19x2 + -7x2 = 0 Combine like terms: 12x + 10x = 22x -25 + 22x + 19x2 + -7x2 = 0 Combine like terms: 19x2 + -7x2 = 12x2 -25 + 22x + 12x2 = 0 Solving -25 + 22x + 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'. -2.083333333 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '2.083333333' to each side of the equation. -2.083333333 + 1.833333333x + 2.083333333 + x2 = 0 + 2.083333333 Reorder the terms: -2.083333333 + 2.083333333 + 1.833333333x + x2 = 0 + 2.083333333 Combine like terms: -2.083333333 + 2.083333333 = 0.000000000 0.000000000 + 1.833333333x + x2 = 0 + 2.083333333 1.833333333x + x2 = 0 + 2.083333333 Combine like terms: 0 + 2.083333333 = 2.083333333 1.833333333x + x2 = 2.083333333 The x term is 1.833333333x. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333x + 0.8402777775 + x2 = 2.083333333 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 2.083333333 + 0.8402777775 Combine like terms: 2.083333333 + 0.8402777775 = 2.9236111105 0.8402777775 + 1.833333333x + x2 = 2.9236111105 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 2.9236111105 Calculate the square root of the right side: 1.709857044 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 1.709857044 and -1.709857044.Subproblem 1
x + 0.9166666665 = 1.709857044 Simplifying x + 0.9166666665 = 1.709857044 Reorder the terms: 0.9166666665 + x = 1.709857044 Solving 0.9166666665 + x = 1.709857044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = 1.709857044 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.709857044 + -0.9166666665 x = 1.709857044 + -0.9166666665 Combine like terms: 1.709857044 + -0.9166666665 = 0.7931903775 x = 0.7931903775 Simplifying x = 0.7931903775Subproblem 2
x + 0.9166666665 = -1.709857044 Simplifying x + 0.9166666665 = -1.709857044 Reorder the terms: 0.9166666665 + x = -1.709857044 Solving 0.9166666665 + x = -1.709857044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = -1.709857044 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.709857044 + -0.9166666665 x = -1.709857044 + -0.9166666665 Combine like terms: -1.709857044 + -0.9166666665 = -2.6265237105 x = -2.6265237105 Simplifying x = -2.6265237105Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7931903775, -2.6265237105}
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