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Simplifying 0.3x2 + 11x + -75 = 105 Reorder the terms: -75 + 11x + 0.3x2 = 105 Solving -75 + 11x + 0.3x2 = 105 Solving for variable 'x'. Reorder the terms: -75 + -105 + 11x + 0.3x2 = 105 + -105 Combine like terms: -75 + -105 = -180 -180 + 11x + 0.3x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -180 + 11x + 0.3x2 = 0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -600 + 36.66666667x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + 36.66666667x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 36.66666667x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 36.66666667x + x2 = 0 + 600 36.66666667x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 36.66666667x + x2 = 600 The x term is 36.66666667x. Take half its coefficient (18.33333334). Square it (336.1111114) and add it to both sides. Add '336.1111114' to each side of the equation. 36.66666667x + 336.1111114 + x2 = 600 + 336.1111114 Reorder the terms: 336.1111114 + 36.66666667x + x2 = 600 + 336.1111114 Combine like terms: 600 + 336.1111114 = 936.1111114 336.1111114 + 36.66666667x + x2 = 936.1111114 Factor a perfect square on the left side: (x + 18.33333334)(x + 18.33333334) = 936.1111114 Calculate the square root of the right side: 30.595932923 Break this problem into two subproblems by setting (x + 18.33333334) equal to 30.595932923 and -30.595932923.Subproblem 1
x + 18.33333334 = 30.595932923 Simplifying x + 18.33333334 = 30.595932923 Reorder the terms: 18.33333334 + x = 30.595932923 Solving 18.33333334 + x = 30.595932923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.33333334' to each side of the equation. 18.33333334 + -18.33333334 + x = 30.595932923 + -18.33333334 Combine like terms: 18.33333334 + -18.33333334 = 0.00000000 0.00000000 + x = 30.595932923 + -18.33333334 x = 30.595932923 + -18.33333334 Combine like terms: 30.595932923 + -18.33333334 = 12.262599583 x = 12.262599583 Simplifying x = 12.262599583Subproblem 2
x + 18.33333334 = -30.595932923 Simplifying x + 18.33333334 = -30.595932923 Reorder the terms: 18.33333334 + x = -30.595932923 Solving 18.33333334 + x = -30.595932923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.33333334' to each side of the equation. 18.33333334 + -18.33333334 + x = -30.595932923 + -18.33333334 Combine like terms: 18.33333334 + -18.33333334 = 0.00000000 0.00000000 + x = -30.595932923 + -18.33333334 x = -30.595932923 + -18.33333334 Combine like terms: -30.595932923 + -18.33333334 = -48.929266263 x = -48.929266263 Simplifying x = -48.929266263Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.262599583, -48.929266263}
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