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Simplifying 380x2 + -13.72x + -19.68 = 0 Reorder the terms: -19.68 + -13.72x + 380x2 = 0 Solving -19.68 + -13.72x + 380x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 380 the coefficient of the squared term: Divide each side by '380'. -0.05178947368 + -0.03610526316x + x2 = 0 Move the constant term to the right: Add '0.05178947368' to each side of the equation. -0.05178947368 + -0.03610526316x + 0.05178947368 + x2 = 0 + 0.05178947368 Reorder the terms: -0.05178947368 + 0.05178947368 + -0.03610526316x + x2 = 0 + 0.05178947368 Combine like terms: -0.05178947368 + 0.05178947368 = 0.00000000000 0.00000000000 + -0.03610526316x + x2 = 0 + 0.05178947368 -0.03610526316x + x2 = 0 + 0.05178947368 Combine like terms: 0 + 0.05178947368 = 0.05178947368 -0.03610526316x + x2 = 0.05178947368 The x term is -0.03610526316x. Take half its coefficient (-0.01805263158). Square it (0.0003258975070) and add it to both sides. Add '0.0003258975070' to each side of the equation. -0.03610526316x + 0.0003258975070 + x2 = 0.05178947368 + 0.0003258975070 Reorder the terms: 0.0003258975070 + -0.03610526316x + x2 = 0.05178947368 + 0.0003258975070 Combine like terms: 0.05178947368 + 0.0003258975070 = 0.052115371187 0.0003258975070 + -0.03610526316x + x2 = 0.052115371187 Factor a perfect square on the left side: (x + -0.01805263158)(x + -0.01805263158) = 0.052115371187 Calculate the square root of the right side: 0.228287913 Break this problem into two subproblems by setting (x + -0.01805263158) equal to 0.228287913 and -0.228287913.Subproblem 1
x + -0.01805263158 = 0.228287913 Simplifying x + -0.01805263158 = 0.228287913 Reorder the terms: -0.01805263158 + x = 0.228287913 Solving -0.01805263158 + x = 0.228287913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01805263158' to each side of the equation. -0.01805263158 + 0.01805263158 + x = 0.228287913 + 0.01805263158 Combine like terms: -0.01805263158 + 0.01805263158 = 0.00000000000 0.00000000000 + x = 0.228287913 + 0.01805263158 x = 0.228287913 + 0.01805263158 Combine like terms: 0.228287913 + 0.01805263158 = 0.24634054458 x = 0.24634054458 Simplifying x = 0.24634054458Subproblem 2
x + -0.01805263158 = -0.228287913 Simplifying x + -0.01805263158 = -0.228287913 Reorder the terms: -0.01805263158 + x = -0.228287913 Solving -0.01805263158 + x = -0.228287913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01805263158' to each side of the equation. -0.01805263158 + 0.01805263158 + x = -0.228287913 + 0.01805263158 Combine like terms: -0.01805263158 + 0.01805263158 = 0.00000000000 0.00000000000 + x = -0.228287913 + 0.01805263158 x = -0.228287913 + 0.01805263158 Combine like terms: -0.228287913 + 0.01805263158 = -0.21023528142 x = -0.21023528142 Simplifying x = -0.21023528142Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24634054458, -0.21023528142}
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