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Simplifying 1.9x2 + 2.3x + -1 = 2 Reorder the terms: -1 + 2.3x + 1.9x2 = 2 Solving -1 + 2.3x + 1.9x2 = 2 Solving for variable 'x'. Reorder the terms: -1 + -2 + 2.3x + 1.9x2 = 2 + -2 Combine like terms: -1 + -2 = -3 -3 + 2.3x + 1.9x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -3 + 2.3x + 1.9x2 = 0 Begin completing the square. Divide all terms by 1.9 the coefficient of the squared term: Divide each side by '1.9'. -1.578947368 + 1.210526316x + x2 = 0 Move the constant term to the right: Add '1.578947368' to each side of the equation. -1.578947368 + 1.210526316x + 1.578947368 + x2 = 0 + 1.578947368 Reorder the terms: -1.578947368 + 1.578947368 + 1.210526316x + x2 = 0 + 1.578947368 Combine like terms: -1.578947368 + 1.578947368 = 0.000000000 0.000000000 + 1.210526316x + x2 = 0 + 1.578947368 1.210526316x + x2 = 0 + 1.578947368 Combine like terms: 0 + 1.578947368 = 1.578947368 1.210526316x + x2 = 1.578947368 The x term is 1.210526316x. Take half its coefficient (0.605263158). Square it (0.3663434904) and add it to both sides. Add '0.3663434904' to each side of the equation. 1.210526316x + 0.3663434904 + x2 = 1.578947368 + 0.3663434904 Reorder the terms: 0.3663434904 + 1.210526316x + x2 = 1.578947368 + 0.3663434904 Combine like terms: 1.578947368 + 0.3663434904 = 1.9452908584 0.3663434904 + 1.210526316x + x2 = 1.9452908584 Factor a perfect square on the left side: (x + 0.605263158)(x + 0.605263158) = 1.9452908584 Calculate the square root of the right side: 1.394736842 Break this problem into two subproblems by setting (x + 0.605263158) equal to 1.394736842 and -1.394736842.Subproblem 1
x + 0.605263158 = 1.394736842 Simplifying x + 0.605263158 = 1.394736842 Reorder the terms: 0.605263158 + x = 1.394736842 Solving 0.605263158 + x = 1.394736842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.605263158' to each side of the equation. 0.605263158 + -0.605263158 + x = 1.394736842 + -0.605263158 Combine like terms: 0.605263158 + -0.605263158 = 0.000000000 0.000000000 + x = 1.394736842 + -0.605263158 x = 1.394736842 + -0.605263158 Combine like terms: 1.394736842 + -0.605263158 = 0.789473684 x = 0.789473684 Simplifying x = 0.789473684Subproblem 2
x + 0.605263158 = -1.394736842 Simplifying x + 0.605263158 = -1.394736842 Reorder the terms: 0.605263158 + x = -1.394736842 Solving 0.605263158 + x = -1.394736842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.605263158' to each side of the equation. 0.605263158 + -0.605263158 + x = -1.394736842 + -0.605263158 Combine like terms: 0.605263158 + -0.605263158 = 0.000000000 0.000000000 + x = -1.394736842 + -0.605263158 x = -1.394736842 + -0.605263158 Combine like terms: -1.394736842 + -0.605263158 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.789473684, -2}
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