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Simplifying (0.00623 + -1x)(0.00414 + -1x) = 0 Multiply (0.00623 + -1x) * (0.00414 + -1x) (0.00623(0.00414 + -1x) + -1x * (0.00414 + -1x)) = 0 ((0.00414 * 0.00623 + -1x * 0.00623) + -1x * (0.00414 + -1x)) = 0 ((0.0000257922 + -0.00623x) + -1x * (0.00414 + -1x)) = 0 (0.0000257922 + -0.00623x + (0.00414 * -1x + -1x * -1x)) = 0 (0.0000257922 + -0.00623x + (-0.00414x + 1x2)) = 0 Combine like terms: -0.00623x + -0.00414x = -0.01037x (0.0000257922 + -0.01037x + 1x2) = 0 Solving 0.0000257922 + -0.01037x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0000257922' to each side of the equation. 0.0000257922 + -0.01037x + -0.0000257922 + x2 = 0 + -0.0000257922 Reorder the terms: 0.0000257922 + -0.0000257922 + -0.01037x + x2 = 0 + -0.0000257922 Combine like terms: 0.0000257922 + -0.0000257922 = 0.0000000000 0.0000000000 + -0.01037x + x2 = 0 + -0.0000257922 -0.01037x + x2 = 0 + -0.0000257922 Combine like terms: 0 + -0.0000257922 = -0.0000257922 -0.01037x + x2 = -0.0000257922 The x term is -0.01037x. Take half its coefficient (-0.005185). Square it (0.000026884225) and add it to both sides. Add '0.000026884225' to each side of the equation. -0.01037x + 0.000026884225 + x2 = -0.0000257922 + 0.000026884225 Reorder the terms: 0.000026884225 + -0.01037x + x2 = -0.0000257922 + 0.000026884225 Combine like terms: -0.0000257922 + 0.000026884225 = 0.000001092025 0.000026884225 + -0.01037x + x2 = 0.000001092025 Factor a perfect square on the left side: (x + -0.005185)(x + -0.005185) = 0.000001092025 Calculate the square root of the right side: 0.001045 Break this problem into two subproblems by setting (x + -0.005185) equal to 0.001045 and -0.001045.Subproblem 1
x + -0.005185 = 0.001045 Simplifying x + -0.005185 = 0.001045 Reorder the terms: -0.005185 + x = 0.001045 Solving -0.005185 + x = 0.001045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005185' to each side of the equation. -0.005185 + 0.005185 + x = 0.001045 + 0.005185 Combine like terms: -0.005185 + 0.005185 = 0.000000 0.000000 + x = 0.001045 + 0.005185 x = 0.001045 + 0.005185 Combine like terms: 0.001045 + 0.005185 = 0.00623 x = 0.00623 Simplifying x = 0.00623Subproblem 2
x + -0.005185 = -0.001045 Simplifying x + -0.005185 = -0.001045 Reorder the terms: -0.005185 + x = -0.001045 Solving -0.005185 + x = -0.001045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005185' to each side of the equation. -0.005185 + 0.005185 + x = -0.001045 + 0.005185 Combine like terms: -0.005185 + 0.005185 = 0.000000 0.000000 + x = -0.001045 + 0.005185 x = -0.001045 + 0.005185 Combine like terms: -0.001045 + 0.005185 = 0.00414 x = 0.00414 Simplifying x = 0.00414Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00623, 0.00414}
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