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Simplifying 12x2 + 35x + 12 = 0 Reorder the terms: 12 + 35x + 12x2 = 0 Solving 12 + 35x + 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 + 2.916666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.916666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.916666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.916666667x + x2 = 0 + -1 2.916666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.916666667x + x2 = -1 The x term is 2.916666667x. Take half its coefficient (1.458333334). Square it (2.126736113) and add it to both sides. Add '2.126736113' to each side of the equation. 2.916666667x + 2.126736113 + x2 = -1 + 2.126736113 Reorder the terms: 2.126736113 + 2.916666667x + x2 = -1 + 2.126736113 Combine like terms: -1 + 2.126736113 = 1.126736113 2.126736113 + 2.916666667x + x2 = 1.126736113 Factor a perfect square on the left side: (x + 1.458333334)(x + 1.458333334) = 1.126736113 Calculate the square root of the right side: 1.061478268 Break this problem into two subproblems by setting (x + 1.458333334) equal to 1.061478268 and -1.061478268.Subproblem 1
x + 1.458333334 = 1.061478268 Simplifying x + 1.458333334 = 1.061478268 Reorder the terms: 1.458333334 + x = 1.061478268 Solving 1.458333334 + x = 1.061478268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.458333334' to each side of the equation. 1.458333334 + -1.458333334 + x = 1.061478268 + -1.458333334 Combine like terms: 1.458333334 + -1.458333334 = 0.000000000 0.000000000 + x = 1.061478268 + -1.458333334 x = 1.061478268 + -1.458333334 Combine like terms: 1.061478268 + -1.458333334 = -0.396855066 x = -0.396855066 Simplifying x = -0.396855066Subproblem 2
x + 1.458333334 = -1.061478268 Simplifying x + 1.458333334 = -1.061478268 Reorder the terms: 1.458333334 + x = -1.061478268 Solving 1.458333334 + x = -1.061478268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.458333334' to each side of the equation. 1.458333334 + -1.458333334 + x = -1.061478268 + -1.458333334 Combine like terms: 1.458333334 + -1.458333334 = 0.000000000 0.000000000 + x = -1.061478268 + -1.458333334 x = -1.061478268 + -1.458333334 Combine like terms: -1.061478268 + -1.458333334 = -2.519811602 x = -2.519811602 Simplifying x = -2.519811602Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.396855066, -2.519811602}
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