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Simplifying -19x2 + 685x + -100 = 0 Reorder the terms: -100 + 685x + -19x2 = 0 Solving -100 + 685x + -19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. 5.263157895 + -36.05263158x + x2 = 0 Move the constant term to the right: Add '-5.263157895' to each side of the equation. 5.263157895 + -36.05263158x + -5.263157895 + x2 = 0 + -5.263157895 Reorder the terms: 5.263157895 + -5.263157895 + -36.05263158x + x2 = 0 + -5.263157895 Combine like terms: 5.263157895 + -5.263157895 = 0.000000000 0.000000000 + -36.05263158x + x2 = 0 + -5.263157895 -36.05263158x + x2 = 0 + -5.263157895 Combine like terms: 0 + -5.263157895 = -5.263157895 -36.05263158x + x2 = -5.263157895 The x term is -36.05263158x. Take half its coefficient (-18.02631579). Square it (324.9480610) and add it to both sides. Add '324.9480610' to each side of the equation. -36.05263158x + 324.9480610 + x2 = -5.263157895 + 324.9480610 Reorder the terms: 324.9480610 + -36.05263158x + x2 = -5.263157895 + 324.9480610 Combine like terms: -5.263157895 + 324.9480610 = 319.684903105 324.9480610 + -36.05263158x + x2 = 319.684903105 Factor a perfect square on the left side: (x + -18.02631579)(x + -18.02631579) = 319.684903105 Calculate the square root of the right side: 17.879734425 Break this problem into two subproblems by setting (x + -18.02631579) equal to 17.879734425 and -17.879734425.Subproblem 1
x + -18.02631579 = 17.879734425 Simplifying x + -18.02631579 = 17.879734425 Reorder the terms: -18.02631579 + x = 17.879734425 Solving -18.02631579 + x = 17.879734425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.02631579' to each side of the equation. -18.02631579 + 18.02631579 + x = 17.879734425 + 18.02631579 Combine like terms: -18.02631579 + 18.02631579 = 0.00000000 0.00000000 + x = 17.879734425 + 18.02631579 x = 17.879734425 + 18.02631579 Combine like terms: 17.879734425 + 18.02631579 = 35.906050215 x = 35.906050215 Simplifying x = 35.906050215Subproblem 2
x + -18.02631579 = -17.879734425 Simplifying x + -18.02631579 = -17.879734425 Reorder the terms: -18.02631579 + x = -17.879734425 Solving -18.02631579 + x = -17.879734425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.02631579' to each side of the equation. -18.02631579 + 18.02631579 + x = -17.879734425 + 18.02631579 Combine like terms: -18.02631579 + 18.02631579 = 0.00000000 0.00000000 + x = -17.879734425 + 18.02631579 x = -17.879734425 + 18.02631579 Combine like terms: -17.879734425 + 18.02631579 = 0.146581365 x = 0.146581365 Simplifying x = 0.146581365Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.906050215, 0.146581365}
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