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Simplifying 12x2 + -9x + -52 = 0 Reorder the terms: -52 + -9x + 12x2 = 0 Solving -52 + -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'. -4.333333333 + -0.75x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -0.75x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -0.75x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -0.75x + x2 = 0 + 4.333333333 -0.75x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -0.75x + x2 = 4.333333333 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 = 4.333333333 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 4.333333333 + 0.140625 Combine like terms: 4.333333333 + 0.140625 = 4.473958333 0.140625 + -0.75x + x2 = 4.473958333 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 4.473958333 Calculate the square root of the right side: 2.115173358 Break this problem into two subproblems by setting (x + -0.375) equal to 2.115173358 and -2.115173358.Subproblem 1
x + -0.375 = 2.115173358 Simplifying x + -0.375 = 2.115173358 Reorder the terms: -0.375 + x = 2.115173358 Solving -0.375 + x = 2.115173358 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 = 2.115173358 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.115173358 + 0.375 x = 2.115173358 + 0.375 Combine like terms: 2.115173358 + 0.375 = 2.490173358 x = 2.490173358 Simplifying x = 2.490173358Subproblem 2
x + -0.375 = -2.115173358 Simplifying x + -0.375 = -2.115173358 Reorder the terms: -0.375 + x = -2.115173358 Solving -0.375 + x = -2.115173358 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 = -2.115173358 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.115173358 + 0.375 x = -2.115173358 + 0.375 Combine like terms: -2.115173358 + 0.375 = -1.740173358 x = -1.740173358 Simplifying x = -1.740173358Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.490173358, -1.740173358}
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