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Simplifying (-6x2 + 3x) + -1(8x2 + 6x + -3) = 0 Reorder the terms: (3x + -6x2) + -1(8x2 + 6x + -3) = 0 Remove parenthesis around (3x + -6x2) 3x + -6x2 + -1(8x2 + 6x + -3) = 0 Reorder the terms: 3x + -6x2 + -1(-3 + 6x + 8x2) = 0 3x + -6x2 + (-3 * -1 + 6x * -1 + 8x2 * -1) = 0 3x + -6x2 + (3 + -6x + -8x2) = 0 Reorder the terms: 3 + 3x + -6x + -6x2 + -8x2 = 0 Combine like terms: 3x + -6x = -3x 3 + -3x + -6x2 + -8x2 = 0 Combine like terms: -6x2 + -8x2 = -14x2 3 + -3x + -14x2 = 0 Solving 3 + -3x + -14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.2142857143 + 0.2142857143x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.2142857143x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.2142857143x + x2 = 0 + 0.2142857143 0.2142857143x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.2142857143x + x2 = 0.2142857143 The x term is 0.2142857143x. Take half its coefficient (0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. 0.2142857143x + 0.01147959185 + x2 = 0.2142857143 + 0.01147959185 Reorder the terms: 0.01147959185 + 0.2142857143x + x2 = 0.2142857143 + 0.01147959185 Combine like terms: 0.2142857143 + 0.01147959185 = 0.22576530615 0.01147959185 + 0.2142857143x + x2 = 0.22576530615 Factor a perfect square on the left side: (x + 0.1071428572)(x + 0.1071428572) = 0.22576530615 Calculate the square root of the right side: 0.475147668 Break this problem into two subproblems by setting (x + 0.1071428572) equal to 0.475147668 and -0.475147668.Subproblem 1
x + 0.1071428572 = 0.475147668 Simplifying x + 0.1071428572 = 0.475147668 Reorder the terms: 0.1071428572 + x = 0.475147668 Solving 0.1071428572 + x = 0.475147668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + x = 0.475147668 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x = 0.475147668 + -0.1071428572 x = 0.475147668 + -0.1071428572 Combine like terms: 0.475147668 + -0.1071428572 = 0.3680048108 x = 0.3680048108 Simplifying x = 0.3680048108Subproblem 2
x + 0.1071428572 = -0.475147668 Simplifying x + 0.1071428572 = -0.475147668 Reorder the terms: 0.1071428572 + x = -0.475147668 Solving 0.1071428572 + x = -0.475147668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + x = -0.475147668 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x = -0.475147668 + -0.1071428572 x = -0.475147668 + -0.1071428572 Combine like terms: -0.475147668 + -0.1071428572 = -0.5822905252 x = -0.5822905252 Simplifying x = -0.5822905252Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3680048108, -0.5822905252}
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