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Simplifying 0.02x2 + 0.05x + -4 = 0 Reorder the terms: -4 + 0.05x + 0.02x2 = 0 Solving -4 + 0.05x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -200 + 2.5x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 2.5x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 2.5x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 2.5x + x2 = 0 + 200 2.5x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 2.5x + x2 = 200 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 200 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 200 + 1.5625 Combine like terms: 200 + 1.5625 = 201.5625 1.5625 + 2.5x + x2 = 201.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 201.5625 Calculate the square root of the right side: 14.197270865 Break this problem into two subproblems by setting (x + 1.25) equal to 14.197270865 and -14.197270865.Subproblem 1
x + 1.25 = 14.197270865 Simplifying x + 1.25 = 14.197270865 Reorder the terms: 1.25 + x = 14.197270865 Solving 1.25 + x = 14.197270865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 14.197270865 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 14.197270865 + -1.25 x = 14.197270865 + -1.25 Combine like terms: 14.197270865 + -1.25 = 12.947270865 x = 12.947270865 Simplifying x = 12.947270865Subproblem 2
x + 1.25 = -14.197270865 Simplifying x + 1.25 = -14.197270865 Reorder the terms: 1.25 + x = -14.197270865 Solving 1.25 + x = -14.197270865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -14.197270865 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -14.197270865 + -1.25 x = -14.197270865 + -1.25 Combine like terms: -14.197270865 + -1.25 = -15.447270865 x = -15.447270865 Simplifying x = -15.447270865Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.947270865, -15.447270865}
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