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Simplifying 0.000000000002028 = 0.02x + 2x2 Solving 0.000000000002028 = 0.02x + 2x2 Solving for variable 'x'. Reorder the terms: 0.000000000002028 + -0.02x + -2x2 = 0.02x + -0.02x + 2x2 + -2x2 Combine like terms: 0.02x + -0.02x = 0.00 0.000000000002028 + -0.02x + -2x2 = 0.00 + 2x2 + -2x2 0.000000000002028 + -0.02x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0.000000000002028 + -0.02x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.000000000001014 + 0.01x + x2 = 0 Move the constant term to the right: Add '0.000000000001014' to each side of the equation. -0.000000000001014 + 0.01x + 0.000000000001014 + x2 = 0 + 0.000000000001014 Reorder the terms: -0.000000000001014 + 0.000000000001014 + 0.01x + x2 = 0 + 0.000000000001014 Combine like terms: -0.000000000001014 + 0.000000000001014 = 0.000000000000000 0.000000000000000 + 0.01x + x2 = 0 + 0.000000000001014 0.01x + x2 = 0 + 0.000000000001014 Combine like terms: 0 + 0.000000000001014 = 0.000000000001014 0.01x + x2 = 0.000000000001014 The x term is 0.01x. Take half its coefficient (0.005). Square it (0.000025) and add it to both sides. Add '0.000025' to each side of the equation. 0.01x + 0.000025 + x2 = 0.000000000001014 + 0.000025 Reorder the terms: 0.000025 + 0.01x + x2 = 0.000000000001014 + 0.000025 Combine like terms: 0.000000000001014 + 0.000025 = 0.000025000001014 0.000025 + 0.01x + x2 = 0.000025000001014 Factor a perfect square on the left side: (x + 0.005)(x + 0.005) = 0.000025000001014 Calculate the square root of the right side: 0.005 Break this problem into two subproblems by setting (x + 0.005) equal to 0.005 and -0.005.Subproblem 1
x + 0.005 = 0.005 Simplifying x + 0.005 = 0.005 Reorder the terms: 0.005 + x = 0.005 Add '-0.005' to each side of the equation. 0.005 + -0.005 + x = 0.005 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = 0.005 + -0.005 x = 0.005 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 x = 0.000 Solving x = 0.000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Simplifying x = 0.000Subproblem 2
x + 0.005 = -0.005 Simplifying x + 0.005 = -0.005 Reorder the terms: 0.005 + x = -0.005 Solving 0.005 + x = -0.005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.005' to each side of the equation. 0.005 + -0.005 + x = -0.005 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = -0.005 + -0.005 x = -0.005 + -0.005 Combine like terms: -0.005 + -0.005 = -0.01 x = -0.01 Simplifying x = -0.01Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000, -0.01}
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