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Simplifying 0.000036 + -0.00072x = x2 Solving 0.000036 + -0.00072x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.000036 + -0.00072x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.000036 + 0.00072x + x2 = 0 Move the constant term to the right: Add '0.000036' to each side of the equation. -0.000036 + 0.00072x + 0.000036 + x2 = 0 + 0.000036 Reorder the terms: -0.000036 + 0.000036 + 0.00072x + x2 = 0 + 0.000036 Combine like terms: -0.000036 + 0.000036 = 0.000000 0.000000 + 0.00072x + x2 = 0 + 0.000036 0.00072x + x2 = 0 + 0.000036 Combine like terms: 0 + 0.000036 = 0.000036 0.00072x + x2 = 0.000036 The x term is 0.00072x. Take half its coefficient (0.00036). Square it (0.0000001296) and add it to both sides. Add '0.0000001296' to each side of the equation. 0.00072x + 0.0000001296 + x2 = 0.000036 + 0.0000001296 Reorder the terms: 0.0000001296 + 0.00072x + x2 = 0.000036 + 0.0000001296 Combine like terms: 0.000036 + 0.0000001296 = 0.0000361296 0.0000001296 + 0.00072x + x2 = 0.0000361296 Factor a perfect square on the left side: (x + 0.00036)(x + 0.00036) = 0.0000361296 Calculate the square root of the right side: 0.00601079 Break this problem into two subproblems by setting (x + 0.00036) equal to 0.00601079 and -0.00601079.Subproblem 1
x + 0.00036 = 0.00601079 Simplifying x + 0.00036 = 0.00601079 Reorder the terms: 0.00036 + x = 0.00601079 Solving 0.00036 + x = 0.00601079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00036' to each side of the equation. 0.00036 + -0.00036 + x = 0.00601079 + -0.00036 Combine like terms: 0.00036 + -0.00036 = 0.00000 0.00000 + x = 0.00601079 + -0.00036 x = 0.00601079 + -0.00036 Combine like terms: 0.00601079 + -0.00036 = 0.00565079 x = 0.00565079 Simplifying x = 0.00565079Subproblem 2
x + 0.00036 = -0.00601079 Simplifying x + 0.00036 = -0.00601079 Reorder the terms: 0.00036 + x = -0.00601079 Solving 0.00036 + x = -0.00601079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00036' to each side of the equation. 0.00036 + -0.00036 + x = -0.00601079 + -0.00036 Combine like terms: 0.00036 + -0.00036 = 0.00000 0.00000 + x = -0.00601079 + -0.00036 x = -0.00601079 + -0.00036 Combine like terms: -0.00601079 + -0.00036 = -0.00637079 x = -0.00637079 Simplifying x = -0.00637079Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00565079, -0.00637079}
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