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Simplifying x2 + 0.015x + -0.009 = 0 Reorder the terms: -0.009 + 0.015x + x2 = 0 Solving -0.009 + 0.015x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.009' to each side of the equation. -0.009 + 0.015x + 0.009 + x2 = 0 + 0.009 Reorder the terms: -0.009 + 0.009 + 0.015x + x2 = 0 + 0.009 Combine like terms: -0.009 + 0.009 = 0.000 0.000 + 0.015x + x2 = 0 + 0.009 0.015x + x2 = 0 + 0.009 Combine like terms: 0 + 0.009 = 0.009 0.015x + x2 = 0.009 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 = 0.009 + 0.00005625 Reorder the terms: 0.00005625 + 0.015x + x2 = 0.009 + 0.00005625 Combine like terms: 0.009 + 0.00005625 = 0.00905625 0.00005625 + 0.015x + x2 = 0.00905625 Factor a perfect square on the left side: (x + 0.0075)(x + 0.0075) = 0.00905625 Calculate the square root of the right side: 0.095164332 Break this problem into two subproblems by setting (x + 0.0075) equal to 0.095164332 and -0.095164332.Subproblem 1
x + 0.0075 = 0.095164332 Simplifying x + 0.0075 = 0.095164332 Reorder the terms: 0.0075 + x = 0.095164332 Solving 0.0075 + x = 0.095164332 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 = 0.095164332 + -0.0075 Combine like terms: 0.0075 + -0.0075 = 0.0000 0.0000 + x = 0.095164332 + -0.0075 x = 0.095164332 + -0.0075 Combine like terms: 0.095164332 + -0.0075 = 0.087664332 x = 0.087664332 Simplifying x = 0.087664332Subproblem 2
x + 0.0075 = -0.095164332 Simplifying x + 0.0075 = -0.095164332 Reorder the terms: 0.0075 + x = -0.095164332 Solving 0.0075 + x = -0.095164332 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 = -0.095164332 + -0.0075 Combine like terms: 0.0075 + -0.0075 = 0.0000 0.0000 + x = -0.095164332 + -0.0075 x = -0.095164332 + -0.0075 Combine like terms: -0.095164332 + -0.0075 = -0.102664332 x = -0.102664332 Simplifying x = -0.102664332Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.087664332, -0.102664332}
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