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Simplifying 12x2 + 9x + -7 = 0 Reorder the terms: -7 + 9x + 12x2 = 0 Solving -7 + 9x + 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 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + 0.75x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + 0.75x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + 0.75x + x2 = 0 + 0.5833333333 0.75x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 0.75x + x2 = 0.5833333333 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.5833333333 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.5833333333 + 0.140625 Combine like terms: 0.5833333333 + 0.140625 = 0.7239583333 0.140625 + 0.75x + x2 = 0.7239583333 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.7239583333 Calculate the square root of the right side: 0.850857411 Break this problem into two subproblems by setting (x + 0.375) equal to 0.850857411 and -0.850857411.Subproblem 1
x + 0.375 = 0.850857411 Simplifying x + 0.375 = 0.850857411 Reorder the terms: 0.375 + x = 0.850857411 Solving 0.375 + x = 0.850857411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.850857411 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.850857411 + -0.375 x = 0.850857411 + -0.375 Combine like terms: 0.850857411 + -0.375 = 0.475857411 x = 0.475857411 Simplifying x = 0.475857411Subproblem 2
x + 0.375 = -0.850857411 Simplifying x + 0.375 = -0.850857411 Reorder the terms: 0.375 + x = -0.850857411 Solving 0.375 + x = -0.850857411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.850857411 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.850857411 + -0.375 x = -0.850857411 + -0.375 Combine like terms: -0.850857411 + -0.375 = -1.225857411 x = -1.225857411 Simplifying x = -1.225857411Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.475857411, -1.225857411}
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