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Simplifying 3x2 + -83x = 105 Reorder the terms: -83x + 3x2 = 105 Solving -83x + 3x2 = 105 Solving for variable 'x'. Reorder the terms: -105 + -83x + 3x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -105 + -83x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -35 + -27.66666667x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -27.66666667x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -27.66666667x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -27.66666667x + x2 = 0 + 35 -27.66666667x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -27.66666667x + x2 = 35 The x term is -27.66666667x. Take half its coefficient (-13.83333334). Square it (191.3611113) and add it to both sides. Add '191.3611113' to each side of the equation. -27.66666667x + 191.3611113 + x2 = 35 + 191.3611113 Reorder the terms: 191.3611113 + -27.66666667x + x2 = 35 + 191.3611113 Combine like terms: 35 + 191.3611113 = 226.3611113 191.3611113 + -27.66666667x + x2 = 226.3611113 Factor a perfect square on the left side: (x + -13.83333334)(x + -13.83333334) = 226.3611113 Calculate the square root of the right side: 15.045301968 Break this problem into two subproblems by setting (x + -13.83333334) equal to 15.045301968 and -15.045301968.Subproblem 1
x + -13.83333334 = 15.045301968 Simplifying x + -13.83333334 = 15.045301968 Reorder the terms: -13.83333334 + x = 15.045301968 Solving -13.83333334 + x = 15.045301968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.83333334' to each side of the equation. -13.83333334 + 13.83333334 + x = 15.045301968 + 13.83333334 Combine like terms: -13.83333334 + 13.83333334 = 0.00000000 0.00000000 + x = 15.045301968 + 13.83333334 x = 15.045301968 + 13.83333334 Combine like terms: 15.045301968 + 13.83333334 = 28.878635308 x = 28.878635308 Simplifying x = 28.878635308Subproblem 2
x + -13.83333334 = -15.045301968 Simplifying x + -13.83333334 = -15.045301968 Reorder the terms: -13.83333334 + x = -15.045301968 Solving -13.83333334 + x = -15.045301968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.83333334' to each side of the equation. -13.83333334 + 13.83333334 + x = -15.045301968 + 13.83333334 Combine like terms: -13.83333334 + 13.83333334 = 0.00000000 0.00000000 + x = -15.045301968 + 13.83333334 x = -15.045301968 + 13.83333334 Combine like terms: -15.045301968 + 13.83333334 = -1.211968628 x = -1.211968628 Simplifying x = -1.211968628Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.878635308, -1.211968628}
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