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Simplifying 0.00016 + -0.0004x = x2 Solving 0.00016 + -0.0004x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.00016 + -0.0004x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.00016 + 0.0004x + x2 = 0 Move the constant term to the right: Add '0.00016' to each side of the equation. -0.00016 + 0.0004x + 0.00016 + x2 = 0 + 0.00016 Reorder the terms: -0.00016 + 0.00016 + 0.0004x + x2 = 0 + 0.00016 Combine like terms: -0.00016 + 0.00016 = 0.00000 0.00000 + 0.0004x + x2 = 0 + 0.00016 0.0004x + x2 = 0 + 0.00016 Combine like terms: 0 + 0.00016 = 0.00016 0.0004x + x2 = 0.00016 The x term is 0.0004x. Take half its coefficient (0.0002). Square it (0.00000004) and add it to both sides. Add '0.00000004' to each side of the equation. 0.0004x + 0.00000004 + x2 = 0.00016 + 0.00000004 Reorder the terms: 0.00000004 + 0.0004x + x2 = 0.00016 + 0.00000004 Combine like terms: 0.00016 + 0.00000004 = 0.00016004 0.00000004 + 0.0004x + x2 = 0.00016004 Factor a perfect square on the left side: (x + 0.0002)(x + 0.0002) = 0.00016004 Calculate the square root of the right side: 0.012650692 Break this problem into two subproblems by setting (x + 0.0002) equal to 0.012650692 and -0.012650692.Subproblem 1
x + 0.0002 = 0.012650692 Simplifying x + 0.0002 = 0.012650692 Reorder the terms: 0.0002 + x = 0.012650692 Solving 0.0002 + x = 0.012650692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0002' to each side of the equation. 0.0002 + -0.0002 + x = 0.012650692 + -0.0002 Combine like terms: 0.0002 + -0.0002 = 0.0000 0.0000 + x = 0.012650692 + -0.0002 x = 0.012650692 + -0.0002 Combine like terms: 0.012650692 + -0.0002 = 0.012450692 x = 0.012450692 Simplifying x = 0.012450692Subproblem 2
x + 0.0002 = -0.012650692 Simplifying x + 0.0002 = -0.012650692 Reorder the terms: 0.0002 + x = -0.012650692 Solving 0.0002 + x = -0.012650692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0002' to each side of the equation. 0.0002 + -0.0002 + x = -0.012650692 + -0.0002 Combine like terms: 0.0002 + -0.0002 = 0.0000 0.0000 + x = -0.012650692 + -0.0002 x = -0.012650692 + -0.0002 Combine like terms: -0.012650692 + -0.0002 = -0.012850692 x = -0.012850692 Simplifying x = -0.012850692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.012450692, -0.012850692}
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