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Simplifying (7x2 + -3x + -43) + (6x2 + 6x) = 0 Reorder the terms: (-43 + -3x + 7x2) + (6x2 + 6x) = 0 Remove parenthesis around (-43 + -3x + 7x2) -43 + -3x + 7x2 + (6x2 + 6x) = 0 Reorder the terms: -43 + -3x + 7x2 + (6x + 6x2) = 0 Remove parenthesis around (6x + 6x2) -43 + -3x + 7x2 + 6x + 6x2 = 0 Reorder the terms: -43 + -3x + 6x + 7x2 + 6x2 = 0 Combine like terms: -3x + 6x = 3x -43 + 3x + 7x2 + 6x2 = 0 Combine like terms: 7x2 + 6x2 = 13x2 -43 + 3x + 13x2 = 0 Solving -43 + 3x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -3.307692308 + 0.2307692308x + x2 = 0 Move the constant term to the right: Add '3.307692308' to each side of the equation. -3.307692308 + 0.2307692308x + 3.307692308 + x2 = 0 + 3.307692308 Reorder the terms: -3.307692308 + 3.307692308 + 0.2307692308x + x2 = 0 + 3.307692308 Combine like terms: -3.307692308 + 3.307692308 = 0.000000000 0.000000000 + 0.2307692308x + x2 = 0 + 3.307692308 0.2307692308x + x2 = 0 + 3.307692308 Combine like terms: 0 + 3.307692308 = 3.307692308 0.2307692308x + x2 = 3.307692308 The x term is 0.2307692308x. Take half its coefficient (0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. 0.2307692308x + 0.01331360947 + x2 = 3.307692308 + 0.01331360947 Reorder the terms: 0.01331360947 + 0.2307692308x + x2 = 3.307692308 + 0.01331360947 Combine like terms: 3.307692308 + 0.01331360947 = 3.32100591747 0.01331360947 + 0.2307692308x + x2 = 3.32100591747 Factor a perfect square on the left side: (x + 0.1153846154)(x + 0.1153846154) = 3.32100591747 Calculate the square root of the right side: 1.822362729 Break this problem into two subproblems by setting (x + 0.1153846154) equal to 1.822362729 and -1.822362729.Subproblem 1
x + 0.1153846154 = 1.822362729 Simplifying x + 0.1153846154 = 1.822362729 Reorder the terms: 0.1153846154 + x = 1.822362729 Solving 0.1153846154 + x = 1.822362729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = 1.822362729 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = 1.822362729 + -0.1153846154 x = 1.822362729 + -0.1153846154 Combine like terms: 1.822362729 + -0.1153846154 = 1.7069781136 x = 1.7069781136 Simplifying x = 1.7069781136Subproblem 2
x + 0.1153846154 = -1.822362729 Simplifying x + 0.1153846154 = -1.822362729 Reorder the terms: 0.1153846154 + x = -1.822362729 Solving 0.1153846154 + x = -1.822362729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = -1.822362729 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = -1.822362729 + -0.1153846154 x = -1.822362729 + -0.1153846154 Combine like terms: -1.822362729 + -0.1153846154 = -1.9377473444 x = -1.9377473444 Simplifying x = -1.9377473444Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7069781136, -1.9377473444}
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