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Simplifying 0.000016 = 2x2 + 0.3x Reorder the terms: 0.000016 = 0.3x + 2x2 Solving 0.000016 = 0.3x + 2x2 Solving for variable 'x'. Reorder the terms: 0.000016 + -0.3x + -2x2 = 0.3x + -0.3x + 2x2 + -2x2 Combine like terms: 0.3x + -0.3x = 0.0 0.000016 + -0.3x + -2x2 = 0.0 + 2x2 + -2x2 0.000016 + -0.3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0.000016 + -0.3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.000008 + 0.15x + x2 = 0 Move the constant term to the right: Add '0.000008' to each side of the equation. -0.000008 + 0.15x + 0.000008 + x2 = 0 + 0.000008 Reorder the terms: -0.000008 + 0.000008 + 0.15x + x2 = 0 + 0.000008 Combine like terms: -0.000008 + 0.000008 = 0.000000 0.000000 + 0.15x + x2 = 0 + 0.000008 0.15x + x2 = 0 + 0.000008 Combine like terms: 0 + 0.000008 = 0.000008 0.15x + x2 = 0.000008 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 0.000008 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 0.000008 + 0.005625 Combine like terms: 0.000008 + 0.005625 = 0.005633 0.005625 + 0.15x + x2 = 0.005633 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.005633 Calculate the square root of the right side: 0.075053314 Break this problem into two subproblems by setting (x + 0.075) equal to 0.075053314 and -0.075053314.Subproblem 1
x + 0.075 = 0.075053314 Simplifying x + 0.075 = 0.075053314 Reorder the terms: 0.075 + x = 0.075053314 Solving 0.075 + x = 0.075053314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.075053314 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.075053314 + -0.075 x = 0.075053314 + -0.075 Combine like terms: 0.075053314 + -0.075 = 0.000053314 x = 0.000053314 Simplifying x = 0.000053314Subproblem 2
x + 0.075 = -0.075053314 Simplifying x + 0.075 = -0.075053314 Reorder the terms: 0.075 + x = -0.075053314 Solving 0.075 + x = -0.075053314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.075053314 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.075053314 + -0.075 x = -0.075053314 + -0.075 Combine like terms: -0.075053314 + -0.075 = -0.150053314 x = -0.150053314 Simplifying x = -0.150053314Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000053314, -0.150053314}
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