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Simplifying 12x2 + -33x + 7 = 0 Reorder the terms: 7 + -33x + 12x2 = 0 Solving 7 + -33x + 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'. 0.5833333333 + -2.75x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + -2.75x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + -2.75x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + -2.75x + x2 = 0 + -0.5833333333 -2.75x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 -2.75x + x2 = -0.5833333333 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = -0.5833333333 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = -0.5833333333 + 1.890625 Combine like terms: -0.5833333333 + 1.890625 = 1.3072916667 1.890625 + -2.75x + x2 = 1.3072916667 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 1.3072916667 Calculate the square root of the right side: 1.143368561 Break this problem into two subproblems by setting (x + -1.375) equal to 1.143368561 and -1.143368561.Subproblem 1
x + -1.375 = 1.143368561 Simplifying x + -1.375 = 1.143368561 Reorder the terms: -1.375 + x = 1.143368561 Solving -1.375 + x = 1.143368561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.143368561 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.143368561 + 1.375 x = 1.143368561 + 1.375 Combine like terms: 1.143368561 + 1.375 = 2.518368561 x = 2.518368561 Simplifying x = 2.518368561Subproblem 2
x + -1.375 = -1.143368561 Simplifying x + -1.375 = -1.143368561 Reorder the terms: -1.375 + x = -1.143368561 Solving -1.375 + x = -1.143368561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.143368561 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.143368561 + 1.375 x = -1.143368561 + 1.375 Combine like terms: -1.143368561 + 1.375 = 0.231631439 x = 0.231631439 Simplifying x = 0.231631439Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.518368561, 0.231631439}
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