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Simplifying 0.00000000000000002 = x(x + 0.1) Reorder the terms: 0.00000000000000002 = x(0.1 + x) 0.00000000000000002 = (0.1 * x + x * x) 0.00000000000000002 = (0.1x + x2) Solving 0.00000000000000002 = 0.1x + x2 Solving for variable 'x'. Reorder the terms: 0.00000000000000002 + -0.1x + -1x2 = 0.1x + -0.1x + x2 + -1x2 Combine like terms: 0.1x + -0.1x = 0.0 0.00000000000000002 + -0.1x + -1x2 = 0.0 + x2 + -1x2 0.00000000000000002 + -0.1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.00000000000000002 + -0.1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.00000000000000002 + 0.1x + x2 = 0 Move the constant term to the right: Add '0.00000000000000002' to each side of the equation. -0.00000000000000002 + 0.1x + 0.00000000000000002 + x2 = 0 + 0.00000000000000002 Reorder the terms: -0.00000000000000002 + 0.00000000000000002 + 0.1x + x2 = 0 + 0.00000000000000002 Combine like terms: -0.00000000000000002 + 0.00000000000000002 = 0.00000000000000000 0.00000000000000000 + 0.1x + x2 = 0 + 0.00000000000000002 0.1x + x2 = 0 + 0.00000000000000002 Combine like terms: 0 + 0.00000000000000002 = 0.00000000000000002 0.1x + x2 = 0.00000000000000002 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.00000000000000002 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.00000000000000002 + 0.0025 Combine like terms: 0.00000000000000002 + 0.0025 = 0.00250000000000002 0.0025 + 0.1x + x2 = 0.00250000000000002 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.00250000000000002 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + 0.05) equal to 0.05 and -0.05.Subproblem 1
x + 0.05 = 0.05 Simplifying x + 0.05 = 0.05 Reorder the terms: 0.05 + x = 0.05 Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.05 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.05 + -0.05 x = 0.05 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 x = 0.00 Solving x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Simplifying x = 0.00Subproblem 2
x + 0.05 = -0.05 Simplifying x + 0.05 = -0.05 Reorder the terms: 0.05 + x = -0.05 Solving 0.05 + x = -0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.05 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.05 + -0.05 x = -0.05 + -0.05 Combine like terms: -0.05 + -0.05 = -0.1 x = -0.1 Simplifying x = -0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00, -0.1}
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