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Simplifying 40x2 + -3x + -0.28 = 0 Reorder the terms: -0.28 + -3x + 40x2 = 0 Solving -0.28 + -3x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.007 + -0.075x + x2 = 0 Move the constant term to the right: Add '0.007' to each side of the equation. -0.007 + -0.075x + 0.007 + x2 = 0 + 0.007 Reorder the terms: -0.007 + 0.007 + -0.075x + x2 = 0 + 0.007 Combine like terms: -0.007 + 0.007 = 0.000 0.000 + -0.075x + x2 = 0 + 0.007 -0.075x + x2 = 0 + 0.007 Combine like terms: 0 + 0.007 = 0.007 -0.075x + x2 = 0.007 The x term is -0.075x. Take half its coefficient (-0.0375). Square it (0.00140625) and add it to both sides. Add '0.00140625' to each side of the equation. -0.075x + 0.00140625 + x2 = 0.007 + 0.00140625 Reorder the terms: 0.00140625 + -0.075x + x2 = 0.007 + 0.00140625 Combine like terms: 0.007 + 0.00140625 = 0.00840625 0.00140625 + -0.075x + x2 = 0.00840625 Factor a perfect square on the left side: (x + -0.0375)(x + -0.0375) = 0.00840625 Calculate the square root of the right side: 0.091685604 Break this problem into two subproblems by setting (x + -0.0375) equal to 0.091685604 and -0.091685604.Subproblem 1
x + -0.0375 = 0.091685604 Simplifying x + -0.0375 = 0.091685604 Reorder the terms: -0.0375 + x = 0.091685604 Solving -0.0375 + x = 0.091685604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0375' to each side of the equation. -0.0375 + 0.0375 + x = 0.091685604 + 0.0375 Combine like terms: -0.0375 + 0.0375 = 0.0000 0.0000 + x = 0.091685604 + 0.0375 x = 0.091685604 + 0.0375 Combine like terms: 0.091685604 + 0.0375 = 0.129185604 x = 0.129185604 Simplifying x = 0.129185604Subproblem 2
x + -0.0375 = -0.091685604 Simplifying x + -0.0375 = -0.091685604 Reorder the terms: -0.0375 + x = -0.091685604 Solving -0.0375 + x = -0.091685604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0375' to each side of the equation. -0.0375 + 0.0375 + x = -0.091685604 + 0.0375 Combine like terms: -0.0375 + 0.0375 = 0.0000 0.0000 + x = -0.091685604 + 0.0375 x = -0.091685604 + 0.0375 Combine like terms: -0.091685604 + 0.0375 = -0.054185604 x = -0.054185604 Simplifying x = -0.054185604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.129185604, -0.054185604}
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