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Simplifying -1.9x2 + -1x + 57 = 0 Reorder the terms: 57 + -1x + -1.9x2 = 0 Solving 57 + -1x + -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'. -30 + 0.5263157895x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 0.5263157895x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 0.5263157895x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 0.5263157895x + x2 = 0 + 30 0.5263157895x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 0.5263157895x + x2 = 30 The x term is 0.5263157895x. Take half its coefficient (0.2631578948). Square it (0.06925207760) and add it to both sides. Add '0.06925207760' to each side of the equation. 0.5263157895x + 0.06925207760 + x2 = 30 + 0.06925207760 Reorder the terms: 0.06925207760 + 0.5263157895x + x2 = 30 + 0.06925207760 Combine like terms: 30 + 0.06925207760 = 30.0692520776 0.06925207760 + 0.5263157895x + x2 = 30.0692520776 Factor a perfect square on the left side: (x + 0.2631578948)(x + 0.2631578948) = 30.0692520776 Calculate the square root of the right side: 5.483543752 Break this problem into two subproblems by setting (x + 0.2631578948) equal to 5.483543752 and -5.483543752.Subproblem 1
x + 0.2631578948 = 5.483543752 Simplifying x + 0.2631578948 = 5.483543752 Reorder the terms: 0.2631578948 + x = 5.483543752 Solving 0.2631578948 + x = 5.483543752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2631578948' to each side of the equation. 0.2631578948 + -0.2631578948 + x = 5.483543752 + -0.2631578948 Combine like terms: 0.2631578948 + -0.2631578948 = 0.0000000000 0.0000000000 + x = 5.483543752 + -0.2631578948 x = 5.483543752 + -0.2631578948 Combine like terms: 5.483543752 + -0.2631578948 = 5.2203858572 x = 5.2203858572 Simplifying x = 5.2203858572Subproblem 2
x + 0.2631578948 = -5.483543752 Simplifying x + 0.2631578948 = -5.483543752 Reorder the terms: 0.2631578948 + x = -5.483543752 Solving 0.2631578948 + x = -5.483543752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2631578948' to each side of the equation. 0.2631578948 + -0.2631578948 + x = -5.483543752 + -0.2631578948 Combine like terms: 0.2631578948 + -0.2631578948 = 0.0000000000 0.0000000000 + x = -5.483543752 + -0.2631578948 x = -5.483543752 + -0.2631578948 Combine like terms: -5.483543752 + -0.2631578948 = -5.7467016468 x = -5.7467016468 Simplifying x = -5.7467016468Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2203858572, -5.7467016468}
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