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Simplifying 12x2 + -39x + 14 = 0 Reorder the terms: 14 + -39x + 12x2 = 0 Solving 14 + -39x + 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 + -3.25x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -3.25x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -3.25x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -3.25x + x2 = 0 + -1.166666667 -3.25x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -3.25x + x2 = -1.166666667 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = -1.166666667 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = -1.166666667 + 2.640625 Combine like terms: -1.166666667 + 2.640625 = 1.473958333 2.640625 + -3.25x + x2 = 1.473958333 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 1.473958333 Calculate the square root of the right side: 1.214066857 Break this problem into two subproblems by setting (x + -1.625) equal to 1.214066857 and -1.214066857.Subproblem 1
x + -1.625 = 1.214066857 Simplifying x + -1.625 = 1.214066857 Reorder the terms: -1.625 + x = 1.214066857 Solving -1.625 + x = 1.214066857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.214066857 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.214066857 + 1.625 x = 1.214066857 + 1.625 Combine like terms: 1.214066857 + 1.625 = 2.839066857 x = 2.839066857 Simplifying x = 2.839066857Subproblem 2
x + -1.625 = -1.214066857 Simplifying x + -1.625 = -1.214066857 Reorder the terms: -1.625 + x = -1.214066857 Solving -1.625 + x = -1.214066857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.214066857 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.214066857 + 1.625 x = -1.214066857 + 1.625 Combine like terms: -1.214066857 + 1.625 = 0.410933143 x = 0.410933143 Simplifying x = 0.410933143Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.839066857, 0.410933143}
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