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Simplifying -1.9X2 + 11.6X + 3.1 = 0 Reorder the terms: 3.1 + 11.6X + -1.9X2 = 0 Solving 3.1 + 11.6X + -1.9X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -1.9 the coefficient of the squared term: Divide each side by '-1.9'. -1.631578947 + -6.105263158X + X2 = 0 Move the constant term to the right: Add '1.631578947' to each side of the equation. -1.631578947 + -6.105263158X + 1.631578947 + X2 = 0 + 1.631578947 Reorder the terms: -1.631578947 + 1.631578947 + -6.105263158X + X2 = 0 + 1.631578947 Combine like terms: -1.631578947 + 1.631578947 = 0.000000000 0.000000000 + -6.105263158X + X2 = 0 + 1.631578947 -6.105263158X + X2 = 0 + 1.631578947 Combine like terms: 0 + 1.631578947 = 1.631578947 -6.105263158X + X2 = 1.631578947 The X term is -6.105263158X. Take half its coefficient (-3.052631579). Square it (9.318559557) and add it to both sides. Add '9.318559557' to each side of the equation. -6.105263158X + 9.318559557 + X2 = 1.631578947 + 9.318559557 Reorder the terms: 9.318559557 + -6.105263158X + X2 = 1.631578947 + 9.318559557 Combine like terms: 1.631578947 + 9.318559557 = 10.950138504 9.318559557 + -6.105263158X + X2 = 10.950138504 Factor a perfect square on the left side: (X + -3.052631579)(X + -3.052631579) = 10.950138504 Calculate the square root of the right side: 3.309099349 Break this problem into two subproblems by setting (X + -3.052631579) equal to 3.309099349 and -3.309099349.Subproblem 1
X + -3.052631579 = 3.309099349 Simplifying X + -3.052631579 = 3.309099349 Reorder the terms: -3.052631579 + X = 3.309099349 Solving -3.052631579 + X = 3.309099349 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.052631579' to each side of the equation. -3.052631579 + 3.052631579 + X = 3.309099349 + 3.052631579 Combine like terms: -3.052631579 + 3.052631579 = 0.000000000 0.000000000 + X = 3.309099349 + 3.052631579 X = 3.309099349 + 3.052631579 Combine like terms: 3.309099349 + 3.052631579 = 6.361730928 X = 6.361730928 Simplifying X = 6.361730928Subproblem 2
X + -3.052631579 = -3.309099349 Simplifying X + -3.052631579 = -3.309099349 Reorder the terms: -3.052631579 + X = -3.309099349 Solving -3.052631579 + X = -3.309099349 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.052631579' to each side of the equation. -3.052631579 + 3.052631579 + X = -3.309099349 + 3.052631579 Combine like terms: -3.052631579 + 3.052631579 = 0.000000000 0.000000000 + X = -3.309099349 + 3.052631579 X = -3.309099349 + 3.052631579 Combine like terms: -3.309099349 + 3.052631579 = -0.25646777 X = -0.25646777 Simplifying X = -0.25646777Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.361730928, -0.25646777}
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