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Simplifying 3x2 + 14x + 12 = 0 Reorder the terms: 12 + 14x + 3x2 = 0 Solving 12 + 14x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.666666667x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 4.666666667x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.666666667x + x2 = 0 + -4 4.666666667x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.666666667x + x2 = -4 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = -4 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -4 + 5.444444448 Combine like terms: -4 + 5.444444448 = 1.444444448 5.444444448 + 4.666666667x + x2 = 1.444444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 1.444444448 Calculate the square root of the right side: 1.201850427 Break this problem into two subproblems by setting (x + 2.333333334) equal to 1.201850427 and -1.201850427.Subproblem 1
x + 2.333333334 = 1.201850427 Simplifying x + 2.333333334 = 1.201850427 Reorder the terms: 2.333333334 + x = 1.201850427 Solving 2.333333334 + x = 1.201850427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 1.201850427 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 1.201850427 + -2.333333334 x = 1.201850427 + -2.333333334 Combine like terms: 1.201850427 + -2.333333334 = -1.131482907 x = -1.131482907 Simplifying x = -1.131482907Subproblem 2
x + 2.333333334 = -1.201850427 Simplifying x + 2.333333334 = -1.201850427 Reorder the terms: 2.333333334 + x = -1.201850427 Solving 2.333333334 + x = -1.201850427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -1.201850427 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -1.201850427 + -2.333333334 x = -1.201850427 + -2.333333334 Combine like terms: -1.201850427 + -2.333333334 = -3.535183761 x = -3.535183761 Simplifying x = -3.535183761Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.131482907, -3.535183761}
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