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Simplifying 72.11x2 + 3490x + -61683.8 = 0 Reorder the terms: -61683.8 + 3490x + 72.11x2 = 0 Solving -61683.8 + 3490x + 72.11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72.11 the coefficient of the squared term: Divide each side by '72.11'. -855.4125641 + 48.3982804x + x2 = 0 Move the constant term to the right: Add '855.4125641' to each side of the equation. -855.4125641 + 48.3982804x + 855.4125641 + x2 = 0 + 855.4125641 Reorder the terms: -855.4125641 + 855.4125641 + 48.3982804x + x2 = 0 + 855.4125641 Combine like terms: -855.4125641 + 855.4125641 = 0.0000000 0.0000000 + 48.3982804x + x2 = 0 + 855.4125641 48.3982804x + x2 = 0 + 855.4125641 Combine like terms: 0 + 855.4125641 = 855.4125641 48.3982804x + x2 = 855.4125641 The x term is 48.3982804x. Take half its coefficient (24.1991402). Square it (585.5983864) and add it to both sides. Add '585.5983864' to each side of the equation. 48.3982804x + 585.5983864 + x2 = 855.4125641 + 585.5983864 Reorder the terms: 585.5983864 + 48.3982804x + x2 = 855.4125641 + 585.5983864 Combine like terms: 855.4125641 + 585.5983864 = 1441.0109505 585.5983864 + 48.3982804x + x2 = 1441.0109505 Factor a perfect square on the left side: (x + 24.1991402)(x + 24.1991402) = 1441.0109505 Calculate the square root of the right side: 37.960650027 Break this problem into two subproblems by setting (x + 24.1991402) equal to 37.960650027 and -37.960650027.Subproblem 1
x + 24.1991402 = 37.960650027 Simplifying x + 24.1991402 = 37.960650027 Reorder the terms: 24.1991402 + x = 37.960650027 Solving 24.1991402 + x = 37.960650027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.1991402' to each side of the equation. 24.1991402 + -24.1991402 + x = 37.960650027 + -24.1991402 Combine like terms: 24.1991402 + -24.1991402 = 0.0000000 0.0000000 + x = 37.960650027 + -24.1991402 x = 37.960650027 + -24.1991402 Combine like terms: 37.960650027 + -24.1991402 = 13.761509827 x = 13.761509827 Simplifying x = 13.761509827Subproblem 2
x + 24.1991402 = -37.960650027 Simplifying x + 24.1991402 = -37.960650027 Reorder the terms: 24.1991402 + x = -37.960650027 Solving 24.1991402 + x = -37.960650027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.1991402' to each side of the equation. 24.1991402 + -24.1991402 + x = -37.960650027 + -24.1991402 Combine like terms: 24.1991402 + -24.1991402 = 0.0000000 0.0000000 + x = -37.960650027 + -24.1991402 x = -37.960650027 + -24.1991402 Combine like terms: -37.960650027 + -24.1991402 = -62.159790227 x = -62.159790227 Simplifying x = -62.159790227Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.761509827, -62.159790227}
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