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Simplifying 0.29x2 + -0.24x + -0.0144 = 0 Reorder the terms: -0.0144 + -0.24x + 0.29x2 = 0 Solving -0.0144 + -0.24x + 0.29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.29 the coefficient of the squared term: Divide each side by '0.29'. -0.04965517241 + -0.8275862069x + x2 = 0 Move the constant term to the right: Add '0.04965517241' to each side of the equation. -0.04965517241 + -0.8275862069x + 0.04965517241 + x2 = 0 + 0.04965517241 Reorder the terms: -0.04965517241 + 0.04965517241 + -0.8275862069x + x2 = 0 + 0.04965517241 Combine like terms: -0.04965517241 + 0.04965517241 = 0.00000000000 0.00000000000 + -0.8275862069x + x2 = 0 + 0.04965517241 -0.8275862069x + x2 = 0 + 0.04965517241 Combine like terms: 0 + 0.04965517241 = 0.04965517241 -0.8275862069x + x2 = 0.04965517241 The x term is -0.8275862069x. Take half its coefficient (-0.4137931035). Square it (0.1712247325) and add it to both sides. Add '0.1712247325' to each side of the equation. -0.8275862069x + 0.1712247325 + x2 = 0.04965517241 + 0.1712247325 Reorder the terms: 0.1712247325 + -0.8275862069x + x2 = 0.04965517241 + 0.1712247325 Combine like terms: 0.04965517241 + 0.1712247325 = 0.22087990491 0.1712247325 + -0.8275862069x + x2 = 0.22087990491 Factor a perfect square on the left side: (x + -0.4137931035)(x + -0.4137931035) = 0.22087990491 Calculate the square root of the right side: 0.469978622 Break this problem into two subproblems by setting (x + -0.4137931035) equal to 0.469978622 and -0.469978622.Subproblem 1
x + -0.4137931035 = 0.469978622 Simplifying x + -0.4137931035 = 0.469978622 Reorder the terms: -0.4137931035 + x = 0.469978622 Solving -0.4137931035 + x = 0.469978622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4137931035' to each side of the equation. -0.4137931035 + 0.4137931035 + x = 0.469978622 + 0.4137931035 Combine like terms: -0.4137931035 + 0.4137931035 = 0.0000000000 0.0000000000 + x = 0.469978622 + 0.4137931035 x = 0.469978622 + 0.4137931035 Combine like terms: 0.469978622 + 0.4137931035 = 0.8837717255 x = 0.8837717255 Simplifying x = 0.8837717255Subproblem 2
x + -0.4137931035 = -0.469978622 Simplifying x + -0.4137931035 = -0.469978622 Reorder the terms: -0.4137931035 + x = -0.469978622 Solving -0.4137931035 + x = -0.469978622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4137931035' to each side of the equation. -0.4137931035 + 0.4137931035 + x = -0.469978622 + 0.4137931035 Combine like terms: -0.4137931035 + 0.4137931035 = 0.0000000000 0.0000000000 + x = -0.469978622 + 0.4137931035 x = -0.469978622 + 0.4137931035 Combine like terms: -0.469978622 + 0.4137931035 = -0.0561855185 x = -0.0561855185 Simplifying x = -0.0561855185Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8837717255, -0.0561855185}
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