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Simplifying (0.00000075) + -1(0.000038x) + -1(4x2) = 0 0.00000075 + -1(0.000038x) + -1(4x2) = 0 Remove parenthesis around (0.000038x) 0.00000075 + -1 * 0.000038x + -1(4x2) = 0 Multiply -1 * 0.000038 0.00000075 + -0.000038x + -1(4x2) = 0 Remove parenthesis around (4x2) 0.00000075 + -0.000038x + -1 * 4x2 = 0 Multiply -1 * 4 0.00000075 + -0.000038x + -4x2 = 0 Solving 0.00000075 + -0.000038x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.0000001875 + 0.0000095x + x2 = 0 Move the constant term to the right: Add '0.0000001875' to each side of the equation. -0.0000001875 + 0.0000095x + 0.0000001875 + x2 = 0 + 0.0000001875 Reorder the terms: -0.0000001875 + 0.0000001875 + 0.0000095x + x2 = 0 + 0.0000001875 Combine like terms: -0.0000001875 + 0.0000001875 = 0.0000000000 0.0000000000 + 0.0000095x + x2 = 0 + 0.0000001875 0.0000095x + x2 = 0 + 0.0000001875 Combine like terms: 0 + 0.0000001875 = 0.0000001875 0.0000095x + x2 = 0.0000001875 The x term is 0.0000095x. Take half its coefficient (0.00000475). Square it (0.0000000000225625) and add it to both sides. Add '0.0000000000225625' to each side of the equation. 0.0000095x + 0.0000000000225625 + x2 = 0.0000001875 + 0.0000000000225625 Reorder the terms: 0.0000000000225625 + 0.0000095x + x2 = 0.0000001875 + 0.0000000000225625 Combine like terms: 0.0000001875 + 0.0000000000225625 = 0.0000001875225625 0.0000000000225625 + 0.0000095x + x2 = 0.0000001875225625 Factor a perfect square on the left side: (x + 0.00000475)(x + 0.00000475) = 0.0000001875225625 Calculate the square root of the right side: 0.000433039 Break this problem into two subproblems by setting (x + 0.00000475) equal to 0.000433039 and -0.000433039.Subproblem 1
x + 0.00000475 = 0.000433039 Simplifying x + 0.00000475 = 0.000433039 Reorder the terms: 0.00000475 + x = 0.000433039 Solving 0.00000475 + x = 0.000433039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000475' to each side of the equation. 0.00000475 + -0.00000475 + x = 0.000433039 + -0.00000475 Combine like terms: 0.00000475 + -0.00000475 = 0.00000000 0.00000000 + x = 0.000433039 + -0.00000475 x = 0.000433039 + -0.00000475 Combine like terms: 0.000433039 + -0.00000475 = 0.000428289 x = 0.000428289 Simplifying x = 0.000428289Subproblem 2
x + 0.00000475 = -0.000433039 Simplifying x + 0.00000475 = -0.000433039 Reorder the terms: 0.00000475 + x = -0.000433039 Solving 0.00000475 + x = -0.000433039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000475' to each side of the equation. 0.00000475 + -0.00000475 + x = -0.000433039 + -0.00000475 Combine like terms: 0.00000475 + -0.00000475 = 0.00000000 0.00000000 + x = -0.000433039 + -0.00000475 x = -0.000433039 + -0.00000475 Combine like terms: -0.000433039 + -0.00000475 = -0.000437789 x = -0.000437789 Simplifying x = -0.000437789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000428289, -0.000437789}
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