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Simplifying 3.4x2 + 60.3x + -1015.7 = 0 Reorder the terms: -1015.7 + 60.3x + 3.4x2 = 0 Solving -1015.7 + 60.3x + 3.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.4 the coefficient of the squared term: Divide each side by '3.4'. -298.7352941 + 17.73529412x + x2 = 0 Move the constant term to the right: Add '298.7352941' to each side of the equation. -298.7352941 + 17.73529412x + 298.7352941 + x2 = 0 + 298.7352941 Reorder the terms: -298.7352941 + 298.7352941 + 17.73529412x + x2 = 0 + 298.7352941 Combine like terms: -298.7352941 + 298.7352941 = 0.0000000 0.0000000 + 17.73529412x + x2 = 0 + 298.7352941 17.73529412x + x2 = 0 + 298.7352941 Combine like terms: 0 + 298.7352941 = 298.7352941 17.73529412x + x2 = 298.7352941 The x term is 17.73529412x. Take half its coefficient (8.86764706). Square it (78.63516438) and add it to both sides. Add '78.63516438' to each side of the equation. 17.73529412x + 78.63516438 + x2 = 298.7352941 + 78.63516438 Reorder the terms: 78.63516438 + 17.73529412x + x2 = 298.7352941 + 78.63516438 Combine like terms: 298.7352941 + 78.63516438 = 377.37045848 78.63516438 + 17.73529412x + x2 = 377.37045848 Factor a perfect square on the left side: (x + 8.86764706)(x + 8.86764706) = 377.37045848 Calculate the square root of the right side: 19.426025288 Break this problem into two subproblems by setting (x + 8.86764706) equal to 19.426025288 and -19.426025288.Subproblem 1
x + 8.86764706 = 19.426025288 Simplifying x + 8.86764706 = 19.426025288 Reorder the terms: 8.86764706 + x = 19.426025288 Solving 8.86764706 + x = 19.426025288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.86764706' to each side of the equation. 8.86764706 + -8.86764706 + x = 19.426025288 + -8.86764706 Combine like terms: 8.86764706 + -8.86764706 = 0.00000000 0.00000000 + x = 19.426025288 + -8.86764706 x = 19.426025288 + -8.86764706 Combine like terms: 19.426025288 + -8.86764706 = 10.558378228 x = 10.558378228 Simplifying x = 10.558378228Subproblem 2
x + 8.86764706 = -19.426025288 Simplifying x + 8.86764706 = -19.426025288 Reorder the terms: 8.86764706 + x = -19.426025288 Solving 8.86764706 + x = -19.426025288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.86764706' to each side of the equation. 8.86764706 + -8.86764706 + x = -19.426025288 + -8.86764706 Combine like terms: 8.86764706 + -8.86764706 = 0.00000000 0.00000000 + x = -19.426025288 + -8.86764706 x = -19.426025288 + -8.86764706 Combine like terms: -19.426025288 + -8.86764706 = -28.293672348 x = -28.293672348 Simplifying x = -28.293672348Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.558378228, -28.293672348}
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