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Simplifying 0 = 2x2 + 0.03x + -0.0001 Reorder the terms: 0 = -0.0001 + 0.03x + 2x2 Solving 0 = -0.0001 + 0.03x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 0.0001 = 0.0001 0.0001 + -0.03x + -2x2 = -0.0001 + 0.03x + 2x2 + 0.0001 + -0.03x + -2x2 Reorder the terms: 0.0001 + -0.03x + -2x2 = -0.0001 + 0.0001 + 0.03x + -0.03x + 2x2 + -2x2 Combine like terms: -0.0001 + 0.0001 = 0.0000 0.0001 + -0.03x + -2x2 = 0.0000 + 0.03x + -0.03x + 2x2 + -2x2 0.0001 + -0.03x + -2x2 = 0.03x + -0.03x + 2x2 + -2x2 Combine like terms: 0.03x + -0.03x = 0.00 0.0001 + -0.03x + -2x2 = 0.00 + 2x2 + -2x2 0.0001 + -0.03x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0.0001 + -0.03x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.00005 + 0.015x + x2 = 0 Move the constant term to the right: Add '0.00005' to each side of the equation. -0.00005 + 0.015x + 0.00005 + x2 = 0 + 0.00005 Reorder the terms: -0.00005 + 0.00005 + 0.015x + x2 = 0 + 0.00005 Combine like terms: -0.00005 + 0.00005 = 0.00000 0.00000 + 0.015x + x2 = 0 + 0.00005 0.015x + x2 = 0 + 0.00005 Combine like terms: 0 + 0.00005 = 0.00005 0.015x + x2 = 0.00005 The x term is 0.015x. Take half its coefficient (0.0075). Square it (0.00005625) and add it to both sides. Add '0.00005625' to each side of the equation. 0.015x + 0.00005625 + x2 = 0.00005 + 0.00005625 Reorder the terms: 0.00005625 + 0.015x + x2 = 0.00005 + 0.00005625 Combine like terms: 0.00005 + 0.00005625 = 0.00010625 0.00005625 + 0.015x + x2 = 0.00010625 Factor a perfect square on the left side: (x + 0.0075)(x + 0.0075) = 0.00010625 Calculate the square root of the right side: 0.010307764 Break this problem into two subproblems by setting (x + 0.0075) equal to 0.010307764 and -0.010307764.Subproblem 1
x + 0.0075 = 0.010307764 Simplifying x + 0.0075 = 0.010307764 Reorder the terms: 0.0075 + x = 0.010307764 Solving 0.0075 + x = 0.010307764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0075' to each side of the equation. 0.0075 + -0.0075 + x = 0.010307764 + -0.0075 Combine like terms: 0.0075 + -0.0075 = 0.0000 0.0000 + x = 0.010307764 + -0.0075 x = 0.010307764 + -0.0075 Combine like terms: 0.010307764 + -0.0075 = 0.002807764 x = 0.002807764 Simplifying x = 0.002807764Subproblem 2
x + 0.0075 = -0.010307764 Simplifying x + 0.0075 = -0.010307764 Reorder the terms: 0.0075 + x = -0.010307764 Solving 0.0075 + x = -0.010307764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0075' to each side of the equation. 0.0075 + -0.0075 + x = -0.010307764 + -0.0075 Combine like terms: 0.0075 + -0.0075 = 0.0000 0.0000 + x = -0.010307764 + -0.0075 x = -0.010307764 + -0.0075 Combine like terms: -0.010307764 + -0.0075 = -0.017807764 x = -0.017807764 Simplifying x = -0.017807764Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002807764, -0.017807764}
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