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Simplifying 9x2 + -28x + -12 = 0 Reorder the terms: -12 + -28x + 9x2 = 0 Solving -12 + -28x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + -3.111111111x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -3.111111111x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -3.111111111x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -3.111111111x + x2 = 0 + 1.333333333 -3.111111111x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -3.111111111x + x2 = 1.333333333 The x term is -3.111111111x. Take half its coefficient (-1.555555556). Square it (2.419753088) and add it to both sides. Add '2.419753088' to each side of the equation. -3.111111111x + 2.419753088 + x2 = 1.333333333 + 2.419753088 Reorder the terms: 2.419753088 + -3.111111111x + x2 = 1.333333333 + 2.419753088 Combine like terms: 1.333333333 + 2.419753088 = 3.753086421 2.419753088 + -3.111111111x + x2 = 3.753086421 Factor a perfect square on the left side: (x + -1.555555556)(x + -1.555555556) = 3.753086421 Calculate the square root of the right side: 1.93728842 Break this problem into two subproblems by setting (x + -1.555555556) equal to 1.93728842 and -1.93728842.Subproblem 1
x + -1.555555556 = 1.93728842 Simplifying x + -1.555555556 = 1.93728842 Reorder the terms: -1.555555556 + x = 1.93728842 Solving -1.555555556 + x = 1.93728842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.555555556' to each side of the equation. -1.555555556 + 1.555555556 + x = 1.93728842 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + x = 1.93728842 + 1.555555556 x = 1.93728842 + 1.555555556 Combine like terms: 1.93728842 + 1.555555556 = 3.492843976 x = 3.492843976 Simplifying x = 3.492843976Subproblem 2
x + -1.555555556 = -1.93728842 Simplifying x + -1.555555556 = -1.93728842 Reorder the terms: -1.555555556 + x = -1.93728842 Solving -1.555555556 + x = -1.93728842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.555555556' to each side of the equation. -1.555555556 + 1.555555556 + x = -1.93728842 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + x = -1.93728842 + 1.555555556 x = -1.93728842 + 1.555555556 Combine like terms: -1.93728842 + 1.555555556 = -0.381732864 x = -0.381732864 Simplifying x = -0.381732864Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.492843976, -0.381732864}
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