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Simplifying 16.3x2 + -197.6x + 7.042 = 0 Reorder the terms: 7.042 + -197.6x + 16.3x2 = 0 Solving 7.042 + -197.6x + 16.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16.3 the coefficient of the squared term: Divide each side by '16.3'. 0.4320245399 + -12.12269939x + x2 = 0 Move the constant term to the right: Add '-0.4320245399' to each side of the equation. 0.4320245399 + -12.12269939x + -0.4320245399 + x2 = 0 + -0.4320245399 Reorder the terms: 0.4320245399 + -0.4320245399 + -12.12269939x + x2 = 0 + -0.4320245399 Combine like terms: 0.4320245399 + -0.4320245399 = 0.0000000000 0.0000000000 + -12.12269939x + x2 = 0 + -0.4320245399 -12.12269939x + x2 = 0 + -0.4320245399 Combine like terms: 0 + -0.4320245399 = -0.4320245399 -12.12269939x + x2 = -0.4320245399 The x term is -12.12269939x. Take half its coefficient (-6.061349695). Square it (36.73996013) and add it to both sides. Add '36.73996013' to each side of the equation. -12.12269939x + 36.73996013 + x2 = -0.4320245399 + 36.73996013 Reorder the terms: 36.73996013 + -12.12269939x + x2 = -0.4320245399 + 36.73996013 Combine like terms: -0.4320245399 + 36.73996013 = 36.3079355901 36.73996013 + -12.12269939x + x2 = 36.3079355901 Factor a perfect square on the left side: (x + -6.061349695)(x + -6.061349695) = 36.3079355901 Calculate the square root of the right side: 6.025606657 Break this problem into two subproblems by setting (x + -6.061349695) equal to 6.025606657 and -6.025606657.Subproblem 1
x + -6.061349695 = 6.025606657 Simplifying x + -6.061349695 = 6.025606657 Reorder the terms: -6.061349695 + x = 6.025606657 Solving -6.061349695 + x = 6.025606657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.061349695' to each side of the equation. -6.061349695 + 6.061349695 + x = 6.025606657 + 6.061349695 Combine like terms: -6.061349695 + 6.061349695 = 0.000000000 0.000000000 + x = 6.025606657 + 6.061349695 x = 6.025606657 + 6.061349695 Combine like terms: 6.025606657 + 6.061349695 = 12.086956352 x = 12.086956352 Simplifying x = 12.086956352Subproblem 2
x + -6.061349695 = -6.025606657 Simplifying x + -6.061349695 = -6.025606657 Reorder the terms: -6.061349695 + x = -6.025606657 Solving -6.061349695 + x = -6.025606657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.061349695' to each side of the equation. -6.061349695 + 6.061349695 + x = -6.025606657 + 6.061349695 Combine like terms: -6.061349695 + 6.061349695 = 0.000000000 0.000000000 + x = -6.025606657 + 6.061349695 x = -6.025606657 + 6.061349695 Combine like terms: -6.025606657 + 6.061349695 = 0.035743038 x = 0.035743038 Simplifying x = 0.035743038Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.086956352, 0.035743038}
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