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Simplifying 0 = 1.2 + 6.6x + 0.5 * 9.82x2 Multiply 0.5 * 9.82 0 = 1.2 + 6.6x + 4.91x2 Solving 0 = 1.2 + 6.6x + 4.91x2 Solving for variable 'x'. Combine like terms: 0 + -1.2 = -1.2 -1.2 + -6.6x + -4.91x2 = 1.2 + 6.6x + 4.91x2 + -1.2 + -6.6x + -4.91x2 Reorder the terms: -1.2 + -6.6x + -4.91x2 = 1.2 + -1.2 + 6.6x + -6.6x + 4.91x2 + -4.91x2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + -6.6x + -4.91x2 = 0.0 + 6.6x + -6.6x + 4.91x2 + -4.91x2 -1.2 + -6.6x + -4.91x2 = 6.6x + -6.6x + 4.91x2 + -4.91x2 Combine like terms: 6.6x + -6.6x = 0.0 -1.2 + -6.6x + -4.91x2 = 0.0 + 4.91x2 + -4.91x2 -1.2 + -6.6x + -4.91x2 = 4.91x2 + -4.91x2 Combine like terms: 4.91x2 + -4.91x2 = 0.00 -1.2 + -6.6x + -4.91x2 = 0.00 Begin completing the square. Divide all terms by -4.91 the coefficient of the squared term: Divide each side by '-4.91'. 0.2443991853 + 1.344195519x + x2 = 0 Move the constant term to the right: Add '-0.2443991853' to each side of the equation. 0.2443991853 + 1.344195519x + -0.2443991853 + x2 = 0 + -0.2443991853 Reorder the terms: 0.2443991853 + -0.2443991853 + 1.344195519x + x2 = 0 + -0.2443991853 Combine like terms: 0.2443991853 + -0.2443991853 = 0.0000000000 0.0000000000 + 1.344195519x + x2 = 0 + -0.2443991853 1.344195519x + x2 = 0 + -0.2443991853 Combine like terms: 0 + -0.2443991853 = -0.2443991853 1.344195519x + x2 = -0.2443991853 The x term is 1.344195519x. Take half its coefficient (0.6720977595). Square it (0.4517153983) and add it to both sides. Add '0.4517153983' to each side of the equation. 1.344195519x + 0.4517153983 + x2 = -0.2443991853 + 0.4517153983 Reorder the terms: 0.4517153983 + 1.344195519x + x2 = -0.2443991853 + 0.4517153983 Combine like terms: -0.2443991853 + 0.4517153983 = 0.207316213 0.4517153983 + 1.344195519x + x2 = 0.207316213 Factor a perfect square on the left side: (x + 0.6720977595)(x + 0.6720977595) = 0.207316213 Calculate the square root of the right side: 0.455319902 Break this problem into two subproblems by setting (x + 0.6720977595) equal to 0.455319902 and -0.455319902.Subproblem 1
x + 0.6720977595 = 0.455319902 Simplifying x + 0.6720977595 = 0.455319902 Reorder the terms: 0.6720977595 + x = 0.455319902 Solving 0.6720977595 + x = 0.455319902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6720977595' to each side of the equation. 0.6720977595 + -0.6720977595 + x = 0.455319902 + -0.6720977595 Combine like terms: 0.6720977595 + -0.6720977595 = 0.0000000000 0.0000000000 + x = 0.455319902 + -0.6720977595 x = 0.455319902 + -0.6720977595 Combine like terms: 0.455319902 + -0.6720977595 = -0.2167778575 x = -0.2167778575 Simplifying x = -0.2167778575Subproblem 2
x + 0.6720977595 = -0.455319902 Simplifying x + 0.6720977595 = -0.455319902 Reorder the terms: 0.6720977595 + x = -0.455319902 Solving 0.6720977595 + x = -0.455319902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6720977595' to each side of the equation. 0.6720977595 + -0.6720977595 + x = -0.455319902 + -0.6720977595 Combine like terms: 0.6720977595 + -0.6720977595 = 0.0000000000 0.0000000000 + x = -0.455319902 + -0.6720977595 x = -0.455319902 + -0.6720977595 Combine like terms: -0.455319902 + -0.6720977595 = -1.1274176615 x = -1.1274176615 Simplifying x = -1.1274176615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2167778575, -1.1274176615}
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