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Simplifying 12x2 + -29x + -14 = 0 Reorder the terms: -14 + -29x + 12x2 = 0 Solving -14 + -29x + 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'. -1.166666667 + -2.416666667x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -2.416666667x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -2.416666667x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -2.416666667x + x2 = 0 + 1.166666667 -2.416666667x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -2.416666667x + x2 = 1.166666667 The x term is -2.416666667x. Take half its coefficient (-1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. -2.416666667x + 1.460069446 + x2 = 1.166666667 + 1.460069446 Reorder the terms: 1.460069446 + -2.416666667x + x2 = 1.166666667 + 1.460069446 Combine like terms: 1.166666667 + 1.460069446 = 2.626736113 1.460069446 + -2.416666667x + x2 = 2.626736113 Factor a perfect square on the left side: (x + -1.208333334)(x + -1.208333334) = 2.626736113 Calculate the square root of the right side: 1.620720862 Break this problem into two subproblems by setting (x + -1.208333334) equal to 1.620720862 and -1.620720862.Subproblem 1
x + -1.208333334 = 1.620720862 Simplifying x + -1.208333334 = 1.620720862 Reorder the terms: -1.208333334 + x = 1.620720862 Solving -1.208333334 + x = 1.620720862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = 1.620720862 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = 1.620720862 + 1.208333334 x = 1.620720862 + 1.208333334 Combine like terms: 1.620720862 + 1.208333334 = 2.829054196 x = 2.829054196 Simplifying x = 2.829054196Subproblem 2
x + -1.208333334 = -1.620720862 Simplifying x + -1.208333334 = -1.620720862 Reorder the terms: -1.208333334 + x = -1.620720862 Solving -1.208333334 + x = -1.620720862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = -1.620720862 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = -1.620720862 + 1.208333334 x = -1.620720862 + 1.208333334 Combine like terms: -1.620720862 + 1.208333334 = -0.412387528 x = -0.412387528 Simplifying x = -0.412387528Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.829054196, -0.412387528}
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