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Simplifying 0 = 12x2 + -35x + -18 Reorder the terms: 0 = -18 + -35x + 12x2 Solving 0 = -18 + -35x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 18 = 18 18 + 35x + -12x2 = -18 + -35x + 12x2 + 18 + 35x + -12x2 Reorder the terms: 18 + 35x + -12x2 = -18 + 18 + -35x + 35x + 12x2 + -12x2 Combine like terms: -18 + 18 = 0 18 + 35x + -12x2 = 0 + -35x + 35x + 12x2 + -12x2 18 + 35x + -12x2 = -35x + 35x + 12x2 + -12x2 Combine like terms: -35x + 35x = 0 18 + 35x + -12x2 = 0 + 12x2 + -12x2 18 + 35x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 18 + 35x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.5 + -2.916666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.916666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.916666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.916666667x + x2 = 0 + 1.5 -2.916666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.916666667x + x2 = 1.5 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 = 1.5 + 2.126736113 Reorder the terms: 2.126736113 + -2.916666667x + x2 = 1.5 + 2.126736113 Combine like terms: 1.5 + 2.126736113 = 3.626736113 2.126736113 + -2.916666667x + x2 = 3.626736113 Factor a perfect square on the left side: (x + -1.458333334)(x + -1.458333334) = 3.626736113 Calculate the square root of the right side: 1.904399148 Break this problem into two subproblems by setting (x + -1.458333334) equal to 1.904399148 and -1.904399148.Subproblem 1
x + -1.458333334 = 1.904399148 Simplifying x + -1.458333334 = 1.904399148 Reorder the terms: -1.458333334 + x = 1.904399148 Solving -1.458333334 + x = 1.904399148 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 = 1.904399148 + 1.458333334 Combine like terms: -1.458333334 + 1.458333334 = 0.000000000 0.000000000 + x = 1.904399148 + 1.458333334 x = 1.904399148 + 1.458333334 Combine like terms: 1.904399148 + 1.458333334 = 3.362732482 x = 3.362732482 Simplifying x = 3.362732482Subproblem 2
x + -1.458333334 = -1.904399148 Simplifying x + -1.458333334 = -1.904399148 Reorder the terms: -1.458333334 + x = -1.904399148 Solving -1.458333334 + x = -1.904399148 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 = -1.904399148 + 1.458333334 Combine like terms: -1.458333334 + 1.458333334 = 0.000000000 0.000000000 + x = -1.904399148 + 1.458333334 x = -1.904399148 + 1.458333334 Combine like terms: -1.904399148 + 1.458333334 = -0.446065814 x = -0.446065814 Simplifying x = -0.446065814Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.362732482, -0.446065814}
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