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Simplifying 2x2 + 0.00000698x + -0.000013262 = 0 Reorder the terms: -0.000013262 + 0.00000698x + 2x2 = 0 Solving -0.000013262 + 0.00000698x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.000006631 + 0.00000349x + x2 = 0 Move the constant term to the right: Add '0.000006631' to each side of the equation. -0.000006631 + 0.00000349x + 0.000006631 + x2 = 0 + 0.000006631 Reorder the terms: -0.000006631 + 0.000006631 + 0.00000349x + x2 = 0 + 0.000006631 Combine like terms: -0.000006631 + 0.000006631 = 0.000000000 0.000000000 + 0.00000349x + x2 = 0 + 0.000006631 0.00000349x + x2 = 0 + 0.000006631 Combine like terms: 0 + 0.000006631 = 0.000006631 0.00000349x + x2 = 0.000006631 The x term is 0.00000349x. Take half its coefficient (0.000001745). Square it (0.000000000003045025) and add it to both sides. Add '0.000000000003045025' to each side of the equation. 0.00000349x + 0.000000000003045025 + x2 = 0.000006631 + 0.000000000003045025 Reorder the terms: 0.000000000003045025 + 0.00000349x + x2 = 0.000006631 + 0.000000000003045025 Combine like terms: 0.000006631 + 0.000000000003045025 = 0.000006631003045025 0.000000000003045025 + 0.00000349x + x2 = 0.000006631003045025 Factor a perfect square on the left side: (x + 0.000001745)(x + 0.000001745) = 0.000006631003045025 Calculate the square root of the right side: 0.002575073 Break this problem into two subproblems by setting (x + 0.000001745) equal to 0.002575073 and -0.002575073.Subproblem 1
x + 0.000001745 = 0.002575073 Simplifying x + 0.000001745 = 0.002575073 Reorder the terms: 0.000001745 + x = 0.002575073 Solving 0.000001745 + x = 0.002575073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000001745' to each side of the equation. 0.000001745 + -0.000001745 + x = 0.002575073 + -0.000001745 Combine like terms: 0.000001745 + -0.000001745 = 0.000000000 0.000000000 + x = 0.002575073 + -0.000001745 x = 0.002575073 + -0.000001745 Combine like terms: 0.002575073 + -0.000001745 = 0.002573328 x = 0.002573328 Simplifying x = 0.002573328Subproblem 2
x + 0.000001745 = -0.002575073 Simplifying x + 0.000001745 = -0.002575073 Reorder the terms: 0.000001745 + x = -0.002575073 Solving 0.000001745 + x = -0.002575073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000001745' to each side of the equation. 0.000001745 + -0.000001745 + x = -0.002575073 + -0.000001745 Combine like terms: 0.000001745 + -0.000001745 = 0.000000000 0.000000000 + x = -0.002575073 + -0.000001745 x = -0.002575073 + -0.000001745 Combine like terms: -0.002575073 + -0.000001745 = -0.002576818 x = -0.002576818 Simplifying x = -0.002576818Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002573328, -0.002576818}
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